— A congressional delegation visiting Kiev said Sunday that Ukrainian officials were deeply concerned by a Russian troop buildup, worried that an unpredictable President Vladimir Putin could make a foray into eastern Ukraine and determined to fight back if he did.

Sen. Kelly Ayotte (R-N.H.) said the United States intends to warn Putin off by providing more help for Ukraine and promising Russia deeper financial pain if it refuses to back off its threatening stance. “We can provide military assistance, small arms, communication equipment, fuel,” Ayotte said at a news conference, adding that the Ukrainian military was in disrepair after years of neglect by now-deposed President Viktor Yanukovych. “We’ll help rebuild it.”

No boots on the ground — ­either American or NATO — were being discussed, she said: “We’re not looking for a military conflict with Russia.”

Rep. Stephen F. Lynch (D-Mass.), who is part of the delegation, said the United States needs to “think long and hard about what has happened here,” referring to U.S. obligations under the 1994 Budapest Memorandum, in which Ukraine gave up its nuclear weapons in return for a guarantee of security from the United States, Britain — and Russia.

If Russia’s annexation of Crimea goes unpunished, Lynch said, the world will send a message to other countries that it is a bad idea to part with nuclear weapons. “That’s the wrong message to send,” he said.

Ayotte said that she supported the sanctions President Obama imposed on Putin’s inner circle last week and that they should now be ratcheted up, aimed at broad swaths of the Russian economy, warning Putin that he will pay a price for further incursions. “I believe sanctions can hurt their economy,” she said.

Sen. Joe Donnelly (D-Ind.) said: “This is not about President Obama or Democrats or Republicans. This is the united people of the United States standing with the Ukrainian people.”

The delegation spent part of the day at the Maidan, the square where protesters gathered in ­November and stayed until ­Yanukovych fled Feb. 22. Many of them remain, even now, to remind the new government that the people are watching them.

They called the memorials to the nearly 100 dead — their pictures affixed to the spots where they were shot — heartbreaking. And they seemed close to being at a loss for words when a 35-year-old man stood up at the end of the news conference and described how he had put his wife and two children into their car and fled Crimea on March 10 after two friends were kidnapped. They, like him, were known to have supported the Maidan movement, not a popular idea in newly Russian-controlled Crimea.

“I’m an ethnic Russian,” Sergei Mokrenyuk said. “I was born in Crimea, and so were my children. But I am a Ukrainian citizen. I had to leave everything behind. When can I return, and sleep again in my own home? When will the United States enforce the Budapest Memorandum?”

The United States will stand by that agreement, Ayotte said.

“We will never accept the Russian occupation of Crimea,” she said. “It may take time, but every Russian will feel the pain. We will find a way for you to return to Crimea.”

Earlier Sunday, in separate interviews on CBS’s “Face the Nation,” Ayotte and Sen. Richard J. Durbin (D-Ill.) said that the United States should provide Ukraine with whatever military equipment it needs to help ensure that Russia does not occupy or attempt to take over any other parts of the country.

“This army in Ukraine was devastated by Yanukovych,” Durbin said. “It is so weak now that there are maybe 6,000 troops ready to go to battle. We’ve got to strengthen them and help them with advice and backing, and it may come to small arms. I’m not ruling that out. Keep it on the table. For the time being, let’s help the Ukrainian army get on its feet as a self-defense force.”

Those comments were later echoed by Rep. Mike Rogers (R-Mich.), chairman of the House Intelligence Committee, in an interview on NBC’s “Meet the Press.”

“We have to take a tough stand with our European partners. There are things we can do that we’re not doing.” Rogers said. “We can do noncombatant military aid that allows them to defend themselves.”

Ayotte said the United States should also look into the possibility of imposing further economic sanctions.

“I think we need to do more with sanctions, including sanctioning the entire financial sector of the Russian economy, as well as looking at the energy sector,” Ayotte said, later adding: “The Russian economy is a one-trick pony. They’re totally focused on natural gas and oil. And so if we were to impose greater sanctions on economic sectors, I think we could have a significant impact on Putin, and then he would get the message.”

Meanwhile, 2012 GOP presidential nominee Mitt Romney sharply criticized President Obama’s handling of the Crimean situation, declaring that Obama’s “naivete” has hurt the United States’ standing internationally.

“There is no question that the president’s naivete with regards to Russia and his faulty judgment about Russia’s intentions and objectives has led to a number of foreign policy challenges,” Romney said during an interview on CBS’s “Face the Nation.” “Having not anticipated Russia’s intentions, the president wasn’t able to shape the kinds of events that may have been able to prevent the kinds of circumstances that you’re seeing in the Ukraine.”

Wesley Lowery in Washington contributed to this report.