Athens — After three days of hard bargaining, the summit of the European Community ended without an agreement on how to solve a single major problem facing it. The 10-nation Community is on the verge of bankruptcy and does not possess the authority to raise more cash to cover its rising deficit.
It will now be up to France, which takes over the presidency from Greece on Jan. 1, to guide its colleagues toward a solution that will head off a collapse of the EC as it is at present constituted.
The previous summit, held in Stuttgart, West Germany, last June 17 to 19, acknowledged the crisis and agreed on four objectives for the Athens meeting:
* To reform the Community's budget system to gain firm control over spending.
* To resolve imbalances in the contributions Community members make to the EC budget, a problem that most concerns Britain, which has said it would veto any reform package that does not reduce its budget share.
* To reduce agricultural spending, which absorbs more than two-thirds of Community resources and has been spiraling out of control in recent years.
* To increase the EC's own resources to allow for the admission of Spain and Portugal and to finance new programs that will ''relaunch the Community.''
''It was not Athens that was a step back, it was Stuttgart, because we put too many things on the fire,'' Italian Prime Minister Bettino Craxi asserted.
The summit began Sunday in an atmosphere of subdued optimism after the French put forth a major proposal designed to control Community spending, thus moving closer to the hard-line stance of Britain and West Germany.
The mood rapidly changed as the meeting became mired in disputes over the agenda, and the various delegations demonstrated little will to compromise on the larger questions. Instead they haggled over details that affected them most.
As early as Monday afternoon, reports began to filter out of the conference room of a major clash between French President Francois Mitterrand and British Prime Minister Margaret Thatcher.
According to these reports, Mr. Mitterrand had become tired of what he viewed as a lack of British flexibility and told Mrs. Thatcher she had begun to ''tire your audience,'' but that France would not accept any agreement out of exhaustion. He then allegedly reminded her that France had won the 100 Years War.
According to one source, a member of the British delegation immediately responded that Napoleon probably thought the same thing before the battle of Waterloo.
The resulting crisis of the EC should not be underestimated. The Community does not have enough money to cover this year's expenses, and the European Parliament may refuse to pass this year's supplementary budget to protest the failure in Athens.
The Community will face an even more acute problem in 1984 as agricultural costs continue to mount. Spain and Portugal, which recently expressed frustration at having to wait so long to join the Community, had hoped the deadline to their accession would be set in Athens. Now they will have to wait even longer.
In a period of extreme international tension, of a near breakdown in US-Soviet communications, of acute West European economic crisis, and of growing doubts about the reliability of Western Europe's security cooperation with the United States, the failure in Athens can only increase political uncertainty in the West.
France, often a major obstructionist in past EC deliberations, has emerged as one of the few countries to make a major effort at compromise. It will have to redouble its efforts if it is to save the Community.
On Tuesday Mitterrand asserted that France would do everything in its power to reach a quick compromise and would use elements of proposals already on the table as a starting point for discussions.
This year's deficit can be covered in the 1984 budget, but EC experts say the Community's resources will run out well before year's end. Thus, there was talk of holding the next EC summit, scheduled for June, as early as March, but only if enough progress has been made to warrant such a meeting.