A Syrian air force pilot on a training mission flew into neighboring Jordan and defected with his Russian-made fighter jet, Jordanian and Syrian officials said, the first such incident during the nearly 15-month-old uprising.

The defection happened as more deadly battles foiled a Red Cross team’s efforts to rescue civilians trapped in Homs city, and amid signs President Bashar al-Assad’s regime was stepping up its fight against the opposition.

A Royal Jordanian Air Force official said a MiG-21 belonging to the Syrian Arab Air Force entered Jordanian skies midmorning and was given permission to land at an air base close to the Syrian border.

“The plane’s commander asked that he be granted the right of political asylum,” said the official, who was cited by the kingdom’s state-controlled news agency.

Later, Jordanian government spokesman Samih Maayatah said the pilot was given asylum.

The Syrian Ministry of Defense identified the pilot as Colonel Hassan Merhi al-Hamadah and said the jet had been on a training mission when communication was lost about 10 minutes before its landing in Jordan.

“The aforementioned pilot is a deserter and traitor to his nation and military honor,” said the ministry in a statement carried by the Syrian state news agency. The ministry also said it has contacted the Jordanians to retrieve the plane. The ministry said the pilot would be punished, but didn’t say whether it was seeking the pilot’s return.

Relations between the two neighbors is already tense, with Jordan hosting nearly 125,000 Syrian refugees, including Syrian military and police defectors. Jordan is also a staunch ally of the U.S., U.K. and Saudi Arabia, all active supporters of the armed opposition now waging an insurgency against Mr. Assad’s regime.

The majority of defections have been from infantry and other ground-based military units—those who have been on the front lines of suppressing the uprising. This month, the United Nations confirmed the use of helicopter gunships against opposition targets, but so far there haven’t been reports of war planes used.

Jeremy Binnie, Middle East and Africa editor at the U.K.-based IHS Jane’s Defense Weekly, said the significance of the defection was still unclear but that based on patterns of past defections by Syrian military personnel—many of whom said they wanted to avoid killing their own people—the pilot might have been motivated by possible Syrian plans to start using war planes against the opposition.

“The regime may be getting desperate,” Mr. Binnie said.

The Pentagon praised the pilot’s decision to defect. Press Secretary George Little said he didn’t know whether the U.S. would have access to the pilot to question him, but he said there have been “countless incidents” of members of the Syrian regime seeking to defect, and predicted more such moves to come.

“We have long called for members of the Syrian armed forces and members of the Syrian regime to defect and abandon their positions rather than be complicit in the regime’s atrocities,” Mr. Little said.

Also on Thursday, European countries moved to abandon, for now, a proposal to order member states to stop and search suspected arms shipments to Syria, diplomats said. The diplomats said the proposal raised too many legal difficulties for a decision to be made by the time of Monday’s meeting of foreign ministers.

On the ground, the Syrian government pressed ahead Thursday with a multipronged offensive against several opposition strongholds around the country, activists said, triggering clashes with rebel fighters.

At least 125 people, including 45 members of the Syrian military, were killed Thursday according to the Syrian Observatory for Human Rights, a U.K.-based opposition group.

It said the highest casualties were tracked in Deraa—a rebel stronghold bordering Jordan where the uprising was ignited last year. In the town of Inkhil alone activists said 17 people were killed by government shelling. The casualties couldn’t be independently verified due to government restrictions on foreign media.

In Homs, another opposition center, at least 10 civilians were killed in clashes when government forces tried to storm the Deir Baalbeh neighborhood, activists said.

A team from the International Committee for the Red Cross (ICRC) and the Syrian Red Crescent tried to enter the historic center of Homs on Thursday to rescue several hundred civilians trapped inside but turned back when they heard nearby gunfire, said Rabab al-Rifaie, a Damascus-based Red Cross official.

Ms. Rifaie, who spoke by telephone, said the team will try again later this week to evacuate the wounded and others who want to leave, and to bring medical supplies.

Another potential humanitarian crisis appeared to be worsening in the town of Douma on the outskirts of Damascus. Activists said that scores of wounded civilians needed to urgently be evacuated, as government forces continue to pound the town with artillery and mortar rounds for an eighth consecutive day.

“They need help, they need doctors, they need blood,” pleaded an activist in a neighboring area who identified herself as Susan Ahmad.

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