Deadly fighting continues in Syria, as Arab and European leaders urged the newly united opposition to seek broader support even after it was recognized by the six-nation Gulf Cooperation Council.

The Britain-based Syrian Observatory for Human Rights said the Syrian air force bombed a rebel-held area near the border with Turkey for a second day Tuesday, killing at least one person and wounding three others.

The reported aerial attack on Ras al-Ain raised the two-day death toll in that region to an estimated 31 people.

Nearly 10,000 Syrians have fled into Turkey since Friday, seeking safety from shelling and bombing.

The Syrian Arab Red Crescent estimates the conflict has also displaced 2.5 million civilians inside Syria. Melissa Fleming, chief spokeswoman of the U.N. High Commissioner for Refugees said that number is likely low and “a very conservative estimate.”

Also Tuesday, the Syrian Observatory said fierce battles and army shelling in and around Damascus killed at least 41 people, most of them civilians.

Meanwhile, the leader of Syria's new opposition coalition called on European states to recognize it as the legitimate government and provide it with funds to buy the weapons it needs to overthrow President Bashar al-Assad.

Rebel fighters inside Syria on Tuesday dismissed Gulf and Western voiced support for a new opposition bloc, expecting little to change on the ground unless they get cash and weapons.

Britain and France appeared to set further conditions, notably for rallying support inside Syria, before they grant full recognition to the opposition National Coalition. Like the United States, Europeans are still reluctant to arm rebel forces which include anti-Western Islamist militants.

French Foreign Minister Laurent Fabius and European Union chief Catherine Ashton expressed support for the new coalition but stopped short of formal recognition, a move that could facilitate more aid to the rebels.

The French minister later said his country would play a leading role in seeking recognition for the National Coalition.

The Arab League reacted similarly, endorsing the group but stopping short of giving it full recognition as the representative of the Syrian people.

Opposition members agreed at a meeting Sunday in Doha to create the umbrella front, which brings together the various opposition factions inside Syria and abroad seeking to oust Mr. Assad.

Human Rights Watch issued a statement Tuesday calling on the new coalition to send a “clear message” to opposition fighters that they must adhere to human rights law. The rights group also urged those financing the opposition or providing weapons to express the same expectations.