Senate Minority Leader Robert J. Dole (R-Kan.) plans to announce today his full support for the Intermediate-Range Nuclear Forces Treaty and has engineered a public blessing from President Reagan, touching off a furious new round of jockeying with Vice President Bush in the race for the Republican presidential nomination, informed sources said yesterday.

The president has agreed to accompany Dole before reporters in the White House press briefing room after a private Oval Office meeting, the sources said. This maneuver has privately riled strategists for Bush, the Republican frontrunner who has been gaining political capital for his support of the treaty signed last week by Reagan and Soviet leader Mikhail Gorbachev.

Dole has said repeatedly in recent weeks that he wanted to study the treaty before giving it his full endorsement. His decision comes as Bush is pressing a full-fledged campaign in Iowa to highlight his support for the treaty -- including fresh television commercials showing Bush with Gorbachev -- and amid evidence that Dole's support in Iowa has suddenly eroded because of his apparent indecision.

Before the Reagan-Gorbachev summit, Dole had a healthy lead over Bush in the high-stakes Iowa battle, which many analysts say Dole must win to successfully challenge the vice president in later contests.

Dole's planned endorsement also illustrates how Reagan is becoming increasingly drawn into the 1988 campaign, regardless of his pledge to remain neutral. Sources said the president approved the Dole appearance on Tuesday after it was recommended by White House Chief of Staff Howard H. Baker Jr. One source said "this was an inside job" by Baker, a former Senate minority leader who believes Dole has a critical role in getting early Senate approval of the treaty.

However, Bush strategists were "appalled" at the idea, another informed source said, and "registered our incredulity" that Reagan would appear alone with Dole. Despite the unhappiness in the Bush camp, the Reagan session with Dole could not be canceled, several sources said.

Bush, whom Reagan routinely calls the best vice president in history and who has frequently used his status as incumbent vice president to advance his political goals, lunched privately with Reagan on Tuesday. Sources said the issue of the Dole meeting was raised by the president during the lunch.

Rich Bond, Bush's deputy campaign director and chief Iowa strategist, said, "George Bush's support of INF and his commercials in Iowa have made Dole like Saul on the road to Damascus. He saw a larger vision -- a loss in Iowa -- and is now trying to save himself."

In a further setback, Bush sources said yesterday that eight of Dole's top Rhode Island backers are planning to announce today they have defected to Bush over the INF issue.

Dole has been dogged by criticism that he is waffling on the new treaty while Bush has proclaimed his unequivocal support and invoked the names of European leaders who back it, including British Prime Minister Margaret Thatcher and West German chancellor Helmut Kohl.

Dole yesterday telephoned Thatcher and Kohl with word of his plans, and discussed it here with visiting Italian Prime Minister Giovanni Goria. A Dole campaign source said the senator also discussed the treaty with former presidents Richard M. Nixon and Gerald R. Ford, former secretary of state Henry Kissinger, Secretary of State George P. Shultz, CIA Director William H. Webster and unidentified Democratic foreign policy specialists.

Sources in both campaigns said Dole's lead over Bush in Iowa has been eroding since last week's summit. Within hours after his breakfast with Gorbachev in the Soviet Embassy, Bush was blitzing the state with satellite television interviews and his aides were hosting press conferences and other events to highlight's Dole's indecision. A new Bush television commercial seeking to exploit the issue began airing in Iowa earlier this week, Bush's first paid ad in the state.

One commercial begins, "There's only been one Republican candidate for president to take the lead in support of the Soviet-American summit and the INF Treaty. That's George Bush." The ad closes with a still photo of Bush shaking hands with Gorbachev. Another begins, "Leadership requires decisions . . ." Staff writers Bill Peterson, Ed Walsh and Lloyd Grove contributed to this report.