West Germany and France today backed the extension of Western European economic sanctions against Argentina and pledged continuing support for Britain in its conflict over the Falkland Islands.

But whether all nine of Britain's partners in the European Community will agree to extend the ban on Argentine imports when it expires Monday still appeared in doubt today. Diplomatic sources in Brussels said Ireland, Denmark and Italy had serious reservations about continuing the sanctions in view of the aggressive military actions taken by Britain as well as Argentina in recent days.

A final decision has been left to a meeting of European foreign ministers Sunday or Monday in Luxembourg.

West German Chancellor Helmut Schmidt and French President Francois Mitterrand, following a meeting today in Hamburg, indicated in remarks to reporters that Britain still enjoyed the solid support of its two most important European allies despite growing jitters about the possibility of more fighting in the South Atlantic.

"The community has no reason to deny Britain solidarity," Mitterrand said. Schmidt said that while neither West Germany nor France liked economic sanctions, "We, like France, will stand at Britain's side in solidarity as long as this conflict continues."

The import ban marked a major diplomatic victory for Britain when it was approved unanimously April 10, shortly after Argentina seized the Falklands. But since hostilities escalated, the Europeans have appeared to qualify their initial unequivocal backing by stressing the need for a peacefully negotiated solution to the crisis.

Both Mitterrand and Schmidt renewed calls for a cease-fire. They urged Argentina to withdraw from the islands and reiterated calls for a diplomatic settlement based on United Nations Security Council resolution 502. The French president added that the question of who is entitled to sovereignty over the territory was somewhat obscure.

Schmidt, whose country is Argentina's biggest European trading partner, noted the good trade relations West Germany has enjoyed with Latin American countries in the past. "We would not like to lose these permanently," he said.