Ukraine’s military pounded rebels on Tuesday who had seized the nation’s second-largest airport and threatened to use precision-guided weaponry to dislodge them from their headquarters, as leaders vowed to deal a decisive blow to the separatists in the eastern part of the country.

A day after candy tycoon Petro Poroshenko was declared the overwhelming winner of a presidential election, Ukrainian leaders were newly resolute in their efforts to squash a rebellion in the nation’s industrial heartland. Poroshenko said he intended to call on the United States for military supplies and training.

Top Ukrainian officials welcomed calls from Russia for talks but said their powerful neighbor was playing a double game by sending militants over the border, an assertion Russia denies. Poroshenko, meanwhile, spoke Tuesday to President Obama and was scheduled to meet with him in Europe next week.

By day’s end, the Ukrainian government had retaken Donetsk’s Sergei Prokofiev International Airport, using Soviet-era fighter jets and attack helicopters, and the rebels were left to count their dead. The fighting that started Monday killed about 50 rebels, Denis Pushilin, a leader of the separatists’ self-declared Donetsk People’s Republic, said in a telephone interview Tuesday afternoon. About 50 civilians also were killed, he said. Neither number was immediately confirmed, although Interior Minister Arsen Avakov said Tuesday that “dozens” of rebels had died.

Pushilin, the separatist leader, said Ukrainian forces were now threatening to end the rebels’ occupation of the Donetsk regional administration building with precision-guided weaponry if they did not lay down their arms. “At the moment the situation is very tense, with a lot of threats from Kiev,” he said.

Russia’s top diplomat, meanwhile, warned Kiev against going any further in its military assault on separatists. Foreign Minister Sergei Lavrov said in Moscow that any escalation would be a “colossal mistake,” according to the news agency Interfax.

In one sign of the aggressive new push against the rebels, Poroshenko said he wanted direct U.S. military aid to bolster his country’s weakened army.

“When your neighbor’s house is burning, you should lend him your hose,” Poroshenko said late Monday in an interview with Jackson Diehl, deputy editorial page editor of The Washington Post.

Invoking President Franklin D. Roosevelt’s World War II-era Lend-Lease program, Poroshenko said: “Now we should create a new security treaty exactly like Lend-Lease. . . . We should cooperate in military technical assistance and in advising assistance. We are ready to fight for independence, and we should build up the armed forces of Ukraine.”

Obama called Poroshenko on Tuesday to “offer the full support of the United States as he seeks to unify and move his country forward,” the White House said.

If Ukrainian officials embraced the United States on Tuesday, they used tough rhetoric against Russia, which they have accused of backing the separatists.

“Russia is exporting terrorism, in the most brutal, unashamed manner possible,” Deputy Foreign Minister Danylo Lubkivsky told reporters in Kiev on Tuesday. He said a convoy of vehicles had attempted early Tuesday to enter Ukraine from Russia.

The Organization for Security and Cooperation in Europe (OSCE) said Tuesday that four of its international election monitors in Donetsk lost contact after being stopped at a separatist checkpoint Monday night and that it has been unable to locate them.

The four Donetsk-based OSCE monitors were on a routine patrol at the border of Luhansk and Donetsk provinces when the organization last made contact with them, said spokesman Michael Bociurkiw. The OSCE has posted about 30 monitors to Donetsk, and the nationalities of the four who have disappeared are Estonian, Swiss, Turkish and Danish, he said.

Another OSCE monitoring team was seized by separatists in the eastern city of Slovyansk last month. The group was freed after more than a week.

In Donetsk, the Ukrainian military used MiG fighter jets and Mi-8 and Mi-24 attack helicopters to press its assault against rebels who had taken the airport early Monday. By late Tuesday, the airport was back in government hands.

“We will carry out these operations until not a single terrorist remains on the territory of Ukraine,” First Deputy Prime Minister Vitaliy Yarema said in Kiev, according to Interfax. He said that the fighting had reached a “turning point” and that Ukraine’s military was making gains.

The rebels “have already realized that making the Ukrainian army angry is tantamount to being one’s own enemy,” Yarema said. “They already had the chance to feel that during yesterday’s fighting at the Donetsk airport.”

If the pro-Russian separatists keep fighting, “precision-guided munitions will be used,” said Vladislav Seleznev, a spokesman for the Ukrainian military’s operations in the east.

On Tuesday morning, all roads to Sergei Prokofiev International Airport were blocked because of sporadic gunfire. A large overturned military-type vehicle with a front wheel blown off was lying on a residential road a few miles from the airport.

In a neighborhood less than half a mile from the airport, Alexander Markhovin, 56, a retired miner, stood outside an addition to his house that was destroyed in the clashes.

He said the fighting started up again about 7 a.m. Tuesday. He and his wife were unharmed, having sheltered in an older part of the house.

“We don’t know what it was because . . . smoke covered everything,” he said, standing in his carport, where they had retrieved what they could, including two icons. “It was smoldering.”

By late Tuesday, an unnerving calm settled over Donetsk, a city of nearly a million people that until this week had largely escaped the violence that had plagued the region. Streets seemed almost deserted, and many people headed out of town to stay with relatives. Shops and cafes were closed well before the 8 p.m. curfew called for by separatist leaders.

Those leaders seemed increasingly under stress, both from the military assault launched from Kiev and from Russian President Vladimir Putin’s willingness to engage with the new Ukrainian leadership.

“We warned Russia and we warned the international community that the elections on the 25th of May would not change the situation,” Donetsk separatist leader Pavel Gubarev said in a video statement posted on his Facebook page, in which he spoke from a room where images of Putin and former Venezuelan president Hugo Chávez were hanging on the wall.

“Poroshenko is again coming to us for more bloodshed,” Gubarev said.

Kunkle reported from Donetsk. Abigail Hauslohner in Moscow and Daniela Deane in London contributed to this report.