Army Gen. Martin Dempsey, chairman of the Joint Chiefs of Staff, testifies on Capitol Hill Tuesday before the Senate Armed Services Committee. (Manuel Balce Ceneta/AP)

The top U.S. military officer expressed openness Tuesday to providing U.S. weapons to Ukrainian forces, joining a growing number of senior American officials who say greater U.S. involvement may be needed in Kiev’s fight against Russian-backed separatists.

“I think we should absolutely consider providing lethal aid,” said Army Gen. Martin Dempsey, chairman of the Joint Chiefs of Staff. “And it ought to be in the context of our NATO allies because [Russian President Vladimir] Putin’s ultimate objective is to fracture NATO.”

Dempsey’s comments came in response to a question from Sen. John McCain (R-Ariz.), a strong proponent of arming Ukrainian forces, as Dempsey and Defense Secretary Ashton B. Carter appeared before the Senate Armed Services Committee to defend President Obama’s proposal for military spending in fiscal 2016.

Although he stopped short of saying he would definitely support providing weapons to the Ukrainian military, it was the first time that Dempsey publicly backed consideration of such a move. His remarks come as the Obama administration intensifies its policy deliberations about possible new steps to aid Ukraine.

“There are some capability gaps that put Ukrainian forces at a real disadvantage, and I think we ought to look for opportunities to provide those capabilities,” Dempsey said, so the two sides “can compete on a level playing field.” He did not say what kind of capabilities the United States might provide.

Both Dempsey and Carter warned of dangerous consequences for U.S. national security if Congress does not shield the Pentagon from spending caps known as sequestration. Maintaining adequate spending is especially important, they told lawmakers, as the United States faces an array of global threats including a resilient Taliban, the Islamic State and the risk of a new Cold War in Europe.

The Obama administration is hoping that a European-brokered cease-fire in Ukraine will hold and allow the government of President Petro Poroshenko and the separatists to resolve the crisis.

While Putin denies direct Russian military involvement in the Ukrainian conflict, a U.S. military commander said this week that about 12,000 Russian soldiers are in eastern Ukraine supporting separatist fighters.

U.S. officials have also suggested that Putin may try to secure a land bridge to the Crimean Peninsula or perhaps seize the Ukrainian port city of Mariupol.

Dempsey said Ukraine’s proximity to its powerful neighbor made it a vulnerable target. “If Russia wants to take Ukraine, it’s going to take it,” Dempsey said.

Such fears have led a growing number of current and former U.S. officials to urge Obama to think hard about providing weapons to Ukraine, which also is struggling with an economy in free fall.

Last week, James R. Clapper Jr., the director of national intelligence, said he was in favor of arming Ukrainian forces, even though such a move might provoke Putin. Carter, in his confirmation hearing last month, said he was “inclined in the direction” of arming Ukrainian forces.

Obama has said he would consider taking that step if diplomatic efforts were to fail. But the president, seeking to end the war in Afghanistan and grappling with a new, more uncertain threat from the Islamic State, has appeared reluctant to wade deeper into a conflict at the margins of Europe.

Obama administration officials also have said they are weighing additional sanctions against Russia in response to what they believe are its actions in Ukraine.

Carol Morello contributed to this report.