The Reagan administration doesn't appear to be backing down in its battle to eliminate all farm subsidies worldwide even though President Reagan ran into stiff opposition to the idea at this week's economic summit.

U.S. Trade Representative Clayton Yeutter is raising the threat that unless the Europeans relent in their opposition, the United States could escalate the already costly farm subsidy battle the two sides are engaged in.Yeutter's comments came at the start of two days of negotiations with America's largest trading partners, Canada, Japan and the 12-nation European Economic Community. Officials said that the talks, which were to end Friday, had made no progress on the contentious farm question.

But they said progress had been made on other issues, like protection of intellectual property rights, removal of barriers to trade in such services as banking, and reform of the process by which trade disagreements get settled.

The discussions by the four countries, taking place at a resort in Minnesota's lake country, were aimed at narrowing the differences between them before a critical trade conference in Montreal in December.

One area where officials said progress had been made was in reforming the process by which the 96-member General Agreement on Tariffs and Trade resolves disputes between countries.

"Everybody is in favor of a better dispute settlement mechanism," said Willy de Clercq, trade representative for the European Community. "We have to make the system run smoother and quicker."

An American official, who spoke on condition his name not be used, suggested that the countries meeting in Montreal could well agree to the removal of some trade barriers as early as 1989.

The current round of trade liberalization talks began in 1986 in Uruguay and is scheduled to end in 1990. The Montreal meeting is aimed at settling as many issues as possible and providing momentum for the two remaining years of negotiations.

But on the No. 1 priority of the United States, reform of agricultural subsidies, all sides agreed they are far apart.