DAMASCUS, Syria — Hundreds of Iraqi refugees boarded buses for home on Tuesday in the first convoy from an Iraqi-funded effort to speed the return of families that fled the country's violence and insecurity.

Many Iraqis have headed back on own their own from Syria and elsewhere as extremist attacks have fallen sharply in Baghdad and other areas. But now the Iraqi government is hoping to accelerate the flow — and draw more attention to the recent drop in violence — by offering to pay for trips home.

The program also seeks to win favor from neighboring countries such as Syria and Jordan that are struggling with an estimated 2.2 million Iraqi refugees. Syria has tightened visa rules for Iraqis in hopes of forcing people to return home and blocking new refugees.

"Baghdad, you are victorious," chanted some Iraqis as they headed for a line of 20 buses that would carry about 800 refugees to the border. From there, Iraqi buses are scheduled to bring them to Baghdad on Wednesday, said according to Mohammed Ali al-Budairi, a coordinator for displaced Iraqis in Syria.

The entire trip can take about 10 hours without interruptions, but the convoy will likely be delayed by checkpoints and security precautions. Details about the protection for the convoy was not immediately disclosed.

Khaled Ibrahim, 45, said he was willing to return to Baghdad after hearing the security situation had improved in the capital. But he acknowledged he could pull up stakes again at the first signs of trouble.

"If I go and discover that the situation is not stable, I will come back" to Syria, said Ibrahim, with his wife, three sons and two daughters in tow.

His elder son Abdullah, 13, looked forward to attending school in Baghdad. "Explosions don't scare me," he chirped.

The first bus left by mid-afternoon from al-Sayda Zeinab, an area in southern Damascus where thousands of Iraqi refugees have lived since the 2003 U.S.-led invasion that toppled Saddam Hussein's regime.

Syrian officials says the country has up to 1.5 million Iraqi refugees, straining its education, health and housing systems. Jordan estimates it has up to 700,000 Iraqis. In addition, the U.N. refugee agency has cited various reports of more than 2.4 million Iraqis displaced inside the country.

Adnan al-Shourifi, the commercial secretary at the Iraqi Embassy in Damascus, described the bus convoy Tuesday as a "test."

Thousands of Iraqis in Syria have headed back home in the past weeks. The U.S. military says attacks across Iraq have fallen to their lowest level since February 2006, attributing this partly to a surge of nearly 30,000 troops earlier this year and cooperation from local groups fighting extremist groups such as al-Qaida in Iraq.

Earlier this month, the Iraqi embassy in Damascus set up 11 registration centers for Iraqis to apply for the trip home. In Jordan, Iraqi ambassador Saad al-Hayyani told The Associated Press that Iraq will give Jordan $8 million to help ease the refugee burden.

In Baghdad, government spokesman Ali al-Dabbagh said the "Iraqi government is eager to have Iraqis return to their country and live a normal, safe life." He said more bus convoys of returning refugees are expected in the coming days.

Officials in Iraq and Syria have said more than 46,000 refugees returned in October and the flow has continued this month. The U.N. High Commissioner for Refugees could not confirm the figures, but said more Iraqis were leaving Syria than arriving — with a daily average of 1,500 departures compared with 500 arrivals.

Sybella Wikes, press officer for the UNHCR in Syria, said the agency doesn't "think it's time" yet for a massive refugee return.

"We certainly can't define the situation as being safe in any area in Iraq," she said.

But she added the organization still would "support any Iraqi who wants to return."

Meanwhile, U.S. Rep. Betty McCollum, D-Minn., arrived in Damascus to stress U.S. "concern about the welfare of displaced Iraqis in Syria and Jordan" and "review the situation of Iraqi refugees," a U.S. Embassy statement said. She planned to hold talks with Syrian officials, non-governmental organizations and other agencies.