In the weeks since the Ukraine crisis began, culminating in Tuesday’s decision by Russia to annex Crimea, President Vladi­mir Putin has ignored every gauntlet the United States and its European allies have laid down. The challenge now facing the Obama administration is whether any measures it is prepared to take can deter Russia from moving beyond Crimea into the rest of Ukraine.

Those measures range from freezing the assets of additional individuals, senior officials and companies, beyond the handful of Russians sanctioned earlier this week, to Iran-style banking and export restrictions, according to current and former administration officials.

The administration was publicly silent about its plans Tuesday, promising new sanctions but not saying what it was preparing or when it would act. European Union leaders are scheduled to consider their own response on Thursday.

But Russia’s audacious moves have already led to a rethinking of the defense posture that has dominated the Western alliance since the end of the Soviet Union nearly a quarter-century ago.

There is now “no doubt that Europe has to invest more in defense and security,” NATO Secretary General Anders Fogh Rasmussen said in an interview. And it is equally certain, he said, that “many Europeans would like a reaffirmation of the U.S. commitment to European security.”

Some experts think the West’s image of invincibility and its ability to stand up for its friends may already have been damaged.

“You can’t say, ‘Don’t do something’ and then have no consequences for doing it,” said a former senior national security official in the Obama administration, who described the current international climate as a “horrible environment for miscalculation.”

For example, the former official said, administration hesi­ta­tion could have significant repercussions in East Asia, where China is engaged in territorial disputes in the South China Sea with a number of U.S. partners. “What would we do if China landed forces?” he asked.

With uncertainty about Russia’s aims in eastern and southern Ukraine, the administration and its allies must be willing to suffer the “short-term pain” of possible international economic upheaval — amid the likelihood that Crimea is already lost to Moscow — if only to make the point, said the former official, who spoke on the condition of anonymity to maintain contacts within the administration.

Sanctions that would affect companies such as Gazprom and Rosneft, Russia’s gas monopoly and the country’s biggest oil firm, respectively, could have an immediate impact on the Russian economy and affect future investment. But the intertwined nature of global trade may give the administration pause as it considers such options.

Rosneft, for example, gave Exxon Mobil a leading role in exploring for oil and gas in Russia’s Arctic in exchange for Exxon’s agreement that Rosneft would acquire a 30 percent interest in 20 exploration blocks in the federally leased deep-water areas of the Gulf of Mexico.

In addition, Rosneft, the world’s largest publicly traded oil company when measured in production, has announced plans to buy Morgan Stanley’s unit for storing and trading petroleum products. The acquisition is subject to U.S. government approval.

But the United States “can’t play this game being so self-deterred,” the former official said. “You’re talking about shaping the international environment.”

For a leader committed to dialogue and multilateralism, President Obama is “suddenly having to deal with problems that people weren’t factoring into the game plan . . . for the second term, let alone the next decade,” said Andrew Weiss, vice president for studies at the Carnegie Endowment for International Peace and a top Russia expert in the George H.W. Bush and Clinton administrations.

Even as the United States has steadily drawn down its military presence in Europe, it has extended defense guarantees to new NATO members in the east — guarantees that were “premised on there not being this kind of monolithic threat to security that Russia might represent,” Weiss said.

“Countries in the immediate neighborhood are really panicked by what Putin has done,” he said. “The process of thinking through options and reassuring them is going to take some time.”

The new, Ukraine-influenced European landscape “throws back all kinds of questions about NATO enlargement and European Union integration,” said Fiona Hill of the Brookings Institution. “It makes people more thoughtful.”

The way the Ukrainian crisis evolved over the past few years is particular food for thought, Hill said. It was Europe, she said, that presented Ukraine with an “either-or proposition” of further integrating with the E.U. or joining the alternative market Putin has sought to establish in the east.

When Ukraine’s Russian-backed government chose Putin, pro-Europe forces there rose up and ousted the president. “We forced [Russia’s] hand, whether we intended to or not,” Hill said.

Obama dispatched Vice President Biden this week to calm anxious allies in Eastern Europe, where Polish Prime Minister Donald Tusk said Tuesday that the Ukrainian situation “is a challenge to the whole world. It is not just Poland, but all of Europe must speak in a strong voice.”

Rasmussen — who flew to Washington on Tuesday for a brief overnight visit that included dinner with Secretary of State John F. Kerry, Defense Secretary Chuck Hagel and Susan Rice, Obama’s national security adviser — said that it was “now quite obvious that [NATO] can’t take stability for granted” in Europe.

A September NATO summit is now likely to focus on the new landscape, Rasmussen said, as will top-level meetings scheduled over the next several weeks.

There is no appetite in this country or in Europe for military intervention on Ukraine’s behalf. But as the Obama administration contemplates new sanctions, it has taken other steps to isolate Russia and to strengthen security in the region and in Ukraine itself.

The White House announced Tuesday that Obama has invited his counterparts from Canada, France, Germany, Italy, Japan, Britain and the European Union to meet as the Group of Seven — pointedly not including Russia in the group, which has been known as the G-8 since 1998 — next week on the margins of a nuclear security summit in The Hague.

The United States has sent 12 additional F-16 fighter jets to Poland to bolster a U.S. aviation detachment there. Six more F-15s and two air refuelers were sent to Lithuania as part of a long-standing air patrol mission to guard the borders of NATO’s Baltic members, and Britain announced this week that it would beef up its patrols when it takes over the mission on rotation next month.

The United States and NATO have promised to provide additional assistance to Ukraine’s military, and Rasmussen said the Ukrainians have given the alliance a list of resources — training and weaponry — that they want.

Steven Mufson contributed to this article.