The final bargaining sessions in the Tokyo round of multilateral trade talks formally got underway yesterday with chief negotiators for the key trading partners expressing hope that an agreement on trade rules for at least the next decade can be worked out by this summer.

Ambassador Robert Strauss, the U.S. Special Trade Representative, told an informal meeting of trade negotiators here, "We have brought these talks forward to the point where we can . . . see them through to a successful end by mid-year."

In separate statement's, Wilhelm Haferkamp, vice president of the Common Market in charge of foreign relations, and Japanese Minister of State for External Economic Affairs Nobuhiko Ushiba proposed July as a target date for concluding the talks.

While it is uncertain whether such an optimistic timetable can be met, Strauss noted that in recent months the protracted negotiations have picked up momentum. Deadlines set for submitting requests and offers on tariff and non-tariff concessions have been met despite initial skepticism, he said.

During the past week, trading partners have been readying their offers on trade barrier reductions on hundreds of manufactured products and some agricultural goods in response to requests for reductions submitted last November.

The United States officially tabled its package of trade concessions early this afternoon. A few countries which have not filed their offers, such as Australia and Switzerland, are expected to do so shortly.

Draft codes on reducing the effects of a number of non-tariff obstacles to trade, such as government purchasing policies and national product standards, were drawn up last December. In this round of the talks, the areas of disagreement remain to be ironed out.

The amount of tariff cuts are yet to be decided by trading partners. But in another step toward reaching agreement, the Common Market's Council of Foreign Ministers in Brussels agreed last week to accept U.S. proposals for tariff cuts averaging about 40 percent. A European official here conceded that the Common Market was hoping for a reduction about 5 percent below that figure. Meanwhile, the chief Japanese trade official noted in his speech to trade negotiators that Japan's tariff reduction offers average more than 40 per cent.

The American trade concessions presented yesterday - "a thick pile of computer printouts," as one trade negotiator described them - are not final, according to Strauss, but rather represent "an aggressive, firm . . . negotiating posture."

How this posture fares will be determined "in some 600 separate, direct negotiating sessions . . . over the next several weeks," according to Ambassador Alonzo MacDonald, the chief American negotiator staying behind in Geneva to do the day-to-day bargaining.

The leading trade representatives declined to be drawn into a discussion of the disagreements which remain to be resolved.

Considerable progress has been made in writing draft codes on non-tariff barriers to trade. Such barriers have been the focal point of this round of talks in contrast to past negotiations, held under the auspices of the General Agreement on Tariffs and Trade, which concentrated on tariff cuts. But conflicting provisions must be worked out before the proposed text is completed. There has been no progress in narrowing fundamental differences between the United States and the Common Market over the so-called safeguard clause of GATT. That provision allows countries to restrict imports if foreign competition is damaging a domestic industry. The Europeans want to apply the restrictions selectively against some, rather than all, importers. Nor have the two sides moved closer over European opopsition to the U.S. imposition of retaliatory duties against subsidized imports.