The Ukraine crisis—and the role of further potential sanctions on Russia—will top the agenda for both Chancellor Angela Merkel and President Barack Obama when the German leader arrives in Washington for a White House meeting this week.

Mr. Obama will press Ms. Merkel to put increased pressure on Russia the longer Moscow violates a deal reached in Geneva this month to de-escalate the crisis and tightens its hold on the breakaway region of Crimea, a senior U.S. administration official said. Mr. Obama will also try to reach agreement with the German leader on what further Kremlin moves would trigger tougher penalties across broad sectors of the Russian economy. (Access an interactive table listing Europe and the U.S.'s latest sanctions in response to Russia's actions in Ukraine.)

But Ms. Merkel will also have an eye on her deeply divided domestic constituency and a politically fragmented European Union, both limiting her willingness to turn up the heat on the Kremlin as much as some critics in the U.S. would like.

In addition to time at the White House—the president has scheduled a total of four hours with the chancellor on Friday for talks, a news conference and lunch—the German chancellor plans meals with U.S. political and business figures and a meeting with International Monetary Fund chief Christine Lagarde about financial help for Ukraine. Ms. Merkel will also address the U.S. Chamber of Commerce to try to win support for a trans-Atlantic free-trade agreement that is being met with stiff opposition in Germany.

The meetings are likely to serve as a reminder of America's diplomatic challenges in Western Europe. More than a decade after Berlin opposed the U.S.-led invasion of Iraq, drone strikes, ongoing detentions at Guantanamo Bay and disclosures about the National Security Agency's surveillance programs have continued to chip away at European attitudes toward the U.S. As a result, Ms. Merkel contends with a domestic political landscape where many voters increasingly question U.S. influence and are skeptical of facing down Russia at America's behest.

The U.S. has stressed its coordination with Europe on sanctions against Russia, but some administration officials have been frustrated with European leaders' hesitance in adopting tougher measures. The White House, for example, delayed its announcement of sanctions Friday, putting it off until Monday, to give European counterparts more time, the senior Obama administration official said.

Foreign-policy analysts have long characterized Ms. Merkel, the leader of Europe's largest economy and a Russian speaker, as the West's best bet for getting through to the Kremlin. Ms. Merkel has talked with Russian PresidentVladimir Putin by phone at least 12 times since mid-February, twice as frequently as Mr. Obama and more than any other European leader. Her country's total trade with Russia, some $100 billion last year, is nearly triple that of the U.S., and social and cultural interconnections run deep.

But senior advisers to Ms. Merkel, outraged by pro-Russian separatists' capture Friday of a German-led group of military observers in eastern Ukraine, acknowledge that Mr. Putin has failed to react to weeks of intense diplomacy by Ms. Merkel and her foreign minister.

"It's not a matter of a lack of contact with the Russians," a German official said Tuesday. "It's a matter of a lack of will on the part of the Russians."

German officials have signaled in recent days they are ready to impose further sanctions if pro-Russian unrest in eastern Ukraine continues to escalate. One point of contention: how to spread the economic impact on Western countries. The U.S. would feel little impact from penalties against the Russian energy sector, for example, while Germany's banking industry would be comparatively unaffected by limitations on financial transactions with Russian entities.

So far, Ms. Merkel's approach to Russia has reflected what Germans refer to as her "politics of small steps"—the sort of consensus-building, low-drama policy-making that won her support in Germany as she steered bailouts for debt-stricken countries in the euro zone in recent years. But that approach has led to criticism from policy analysts and politicians on both sides of the Atlantic who say Ms. Merkel needs to show more resolve.

U.S. officials are reluctant to criticize Germany's less aggressive approach so far, instead stressing their support for a step-by-step strategy in dealing with Russia. "The question becomes: what is the content of that at each step," the senior Obama administration official said. "And that'll be part of the conversation."

People close to Ms. Merkel say pursuing "small steps" continues to be as necessary as ever in the Ukraine crisis, with EU countries holding vastly different views on the crisis. German officials say that one of Ms. Merkel's main tasks is to help get all 28 countries in the bloc on the same page, with the Baltics and Poland seeking a hard line against Russia and countries with still-fragile economies or high dependence on Russian energy worried about the consequences of more sanctions.

"Many Germans don't want to believe that the big brother is weaker than we would like," said Josef Braml, a U.S. specialist at the German Council on Foreign Relations. "The truth is that we're the ones who have to face the challenge of what is going on in Ukraine."

Mr. Obama's aides have said Ms. Merkel is one of the few foreign leaders with whom he has a close relationship. U.S. officials say the relationship hasn't been strained by any differences between the U.S. and Europe over the approach to Ukraine.

Friday will be the first one-on-one meeting between the U.S. and German leaders since Mr. Obama visited Berlin last year. The president invited Ms. Merkel to the White House in a phone call in January, before tensions in Ukraine spiraled into a full-blown confrontation. At the time, Berlin was still reeling from revelations that the NSA had monitored Ms. Merkel's cellphone.

The NSA affair remains a charged topic in German politics. Ms. Merkel's government is required to respond by Friday to a parliamentary proposal to invite Edward Snowden, the source of the NSA leaks, to Germany to testify before a parliamentary panel.

On Tuesday, German officials briefing reporters about Ms. Merkel's trip said the chancellor planned to address the NSA issue in her meeting with Mr. Obama. They warned that they expected no breakthroughs on matters Berlin has been pushing for—from a "no-spy" agreement to a promise that U.S. surveillance agencies operating on German soil would respect Germany's strict data privacy protections. And U.S. officials said they were told by their German counterparts that surveillance wouldn't be a top item on Ms. Merkel's agenda.

But in a reflection of the continuing interest in the issue in Germany, the officials in Berlin fielded roughly as many questions from German reporters about the NSA affair as they did about Ukraine.

Write to Anton Troianovski at anton.troianovski@wsj.com and Carol E. Lee atcarol.lee@wsj.com

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