Gov. Michael S. Dukakis, the Democratic presidential nominee, and his running mate Sen. Lloyd M. Bentsen turned up the heat yesterday in a get-tough campaign against their rival, Vice President George Bush, who buoyantly prepared for a cross-country tour of industrial states rich in electoral votes.

Dukakis, spending the weekend in Boston, accused several of the vice president's closest aides of using the White House as a "back door for foreign lobbyists" and declared that "in a Dukakis White House, the staff will pledge allegiance to only one flag--Old Glory."

Preceding Bush to Los Angeles, Bentsen inspected evidence of gang violence--guns, knives and a bullet-riddled car--which he said had increased during the Reagan administration. Bentsen said Bush had led the war against drugs as vice president and "blew it badly."

The GOP nominee, elated by an eight-point lead over Dukakis in public opinion polls, relaxed at his Washington home this weekend before leaving tomorrow for appearances in New Jersey, Illinois, Missouri, California and Ohio.

Bush also planned to announce the formation of a national security advisory task force including former Secretary of State Henry A. Kissinger, former U.N. ambassador Jeane Kirkpatrick, former national security adviser Brent Scowcroft and Zbigniew Brzezinski, who was President Carter's national security adviser.

"I mean to win this election," Bush said repeatedly last week. And Dukakis finally heeded his worried supporters' pleas to take a more combative, aggressive stance against Bush.

The Democratic nominee stepped up the attack at a news conference yesterday in which he denounced the vice president for employing three senior advisers who also are partners in a Washington lobbying firm hired by the government of the Bahamas to improve its image among Reagan administration officials.

Dukakis released a memo by the firm of Charles R. Black, Paul J. Manafort and Roger J. Stone which boasted of the company's influence inside the administration and listed more than a dozen contacts in Bush's office.

The firm received $800,000 in 1985 and 1986 from the Bahamian government. The Bahamian prime minister, Lynden O. Pindling, has long been suspected of involvement with drug traffickers.

"The measure of a president is the quality and integrity of the people with whom he surrounds himself," Dukakis said. "The American people have the right to know that the back door of the White House will not be the front door for paid agents of foreign governments. In a Dukakis White House, there will be no back doors for foreign lobbyists."

Dukakis referred to other campaign aides who reportedly have been sympathetic to Nazis and Nazi organizations, including Jerome Brentar, who resigned as co-chairman of a Bush campaign organization for ethnic groups when it was disclosed that he once defended convicted Nazi war criminal John Demjanjuk.

"I think it says a great deal about that campaign," Dukakis said. "It says a great deal about the judgment of Mr. Bush."

Dukakis also twitted Bush Business president of the Senate for never proposing that senators recite the Pledge of Allegiance as part of their legislative business.

That comment, and his reference to pledging allegiance to only one flag, was the nominee's response to Bush's frequent criticism of Dukakis for vetoing a state bill aimed at requiring public school teachers to lead their classes in reciting the pledge. Dukakis says he was advised that the bill was unconstitutional.

Bentsen toured the Los Angeles Country Sheriff's "Operation Safe Streets" program in the Carson area, a major site of violent gang activities, and took the occasion to blast Bush's role in the administration's anti-drug campaign.