The chief trade negotiators for the United States and its major trading partners began a final round of talks yesterday aimed at hammering out a broad agreement on some of the remaining issues in the multilateral trade talks now going on in Geneva.

Although none of the major participants would comment formally, sources said the negotiators made only modest progress yesterday afternoon, and were expected to talk further at a dinner last night at the Watergate home of U.S. trade chief Robert Strauss.

The negotiators - including Strauss, Wilhelm Haferkamp of the European Common Market, Nobuhiko Ushiba of Japan and Jack Warren of Canada - are hoping to work out a broad framework for a big-power package on trade that can be presented to the seven-nation economic summit July 16-17.

If the package is endorsed by the seven heads of government attending the Bonn summit, officials say the trade talks could come to a close relatively quickly. The Geneva negotiations were begun in 1973, but were stalemated until last year.

Proposals already accepted informally by the big industrial nations include tariff cuts averaging 35 to 40 percent over the next eight to 10 years, and - more important - a reduction in other trade barriers such as subsidies and import-limiting product standards.

However, U.S. officials argue they will need even larger concessions to sell the package to Congress. The American shopping list includes larger tariff cuts, particularly by Japan, European acceptance of more U.S. farm products, and open bidding for foreign government contracts.

Strauss reinforced that theme at a private conference here sponsored by the National Journal, a weekly magazine, asserting that negotiators would be "hard pushed" to meet the mid-July deadline. Strauss termed the talks "tough."

The meetings this week are regarded as the last major effort before the coming Bonn Summit to work out a broad agreement among the major trading powers.