Britain and Guatemala issued a community today in which both sides pledged to seek a peaceful solution to their dispute over Belize, the British colony in the Caribbean to which Guatemala has laid claim.

The communique followed two days of talks between British Minister of State Ted Rowlands and Guatemalan officials.

The generally relaxed atmosphere of the discussions triggered speculation that a quick agreement was reached between Rowlands and President Kjeil Laugerud Garcia at a two-hour meeting they held on Tuesday, the day Rowlands arrived.

Earlier this month Guatemala threatened to invade Belize unless a round of negotiations scheduled for Washington at that time produced significant progress. Britain rushed reinforcements to the colony, formerly called British Honduras.

The main Guatemalen objective in the talks just concluded had been to seek a withdrawal of the British reinforcement. Questioned by reporters on his departure from the airport here, Rowlands said about the level of British forces, "the minimum necessary for defense" would remain until the controversy was settled.

The British had sought mainly a reduction in the possibility of war, and it appears that have gotten it. Rowlands, referring to the first point of the communique, told reporters, "We will carry on negotiating . . . This is the most important decision we have reached."

He said that for now the negotiations will be continued through normal diplomatic channels. Talks at a higher level, he said, generate too much publicity and often raise hopes unnecessarily.

He said that real progress had been made but that the gap between the two countries' positions "is still very considerable."

Powerful factions within the Guatemalan government continue to pressure for a takeover of the colony. Vice President Sandoval Alarcon is currently touring South America to obtain support for the Guatemalan position.