CINCINNATI—Vice President-elect Mike Pence said Thursday that the incoming Trump administration is planning a burst of activity that would take aim at the gridlock in Washington, pressing forward with its goals to overhaul the tax code, health care and immigration laws.

In an interview with The Wall Street Journal, Mr. Pence said President-elect Donald Trump is preparing ambitious 100-day and 200-day plans aimed at fulfilling core campaign promises and jump-starting economic growth.

Asked what might surprise voters about the Trump White House, Mr. Pence said: “I think the only thing that will surprise them is that Washington, D.C., is going to get an awful lot done in a short period of time.”

Mr. Pence spoke in a holding room after introducing Mr. Trump at a rally in Cincinnati, the start of a “thank you” tour in battleground states crucial to the Republican ticket’s victory over Democratic nominee Hillary Clinton in November. As he talked, Mr. Trump could be heard in the background at the U.S. Bank Arena, reviving key lines from his successful campaign stump speeches to enthusiastic cheers.

The agenda laid out by Mr. Pence points to an activist White House that would capitalize on Republican congressional majorities that spent years battling Democratic President Barack Obama.

His comments also suggest that a Trump White House would eschew many of the free-market principles that have guided prior Republican administrations, including injecting itself into the personnel and long-term operating decisions of individual companies.

The new administration’s first priorities would include curbing illegal immigration, abolishing and then replacing Mr. Obama’s signature health-care system, nominating a justice to fill a vacancy on the Supreme Court, and strengthening the military, said Mr. Pence, whose wife, Karen Pence, sat nearby during the interview.

By springtime, the Trump administration would work with congressional leaders “to move fundamental tax reform” meant to “free up the pent-up energy in the American economy,” he said.

Pillars of the tax overhaul would include lowering marginal tax rates, reducing the corporate tax rate “from some of the highest in the industrialized world” to 15%, and repatriating corporate cash held overseas, he said.

Such measures would “benefit American workers and strengthen American incomes,” said Mr. Pence, who will soon relinquish his post as governor of Indiana.

Mr. Pence is positioned to be an active vice president wielding substantial influence in the Trump administration.

Asked if he saw himself in the mold of such previous running mates as Dick Cheney or George H.W. Bush, he said he “can learn a great deal from vice presidents over the last 30 and 40 years. But ultimately I have a firm conviction that the president [Mr. Trump] will define that role. Not me.”

Trump’s Inner Circle

A former congressman, Mr. Pence has made regular trips to Capitol Hill since the election, plotting strategy with legislative leaders. He suggested that part of his value to Mr. Trump is the contacts he has made through years in elective office, both in Washington and at the state level.

“I think those relationships were part of what the president-elect saw that I brought to the team, and at his direction I’m happy to call on those relationships to advance the president’s agenda,” he said.

He described Mr. Trump as a hands-on executive. The pair had come from Indiana, where they celebrated the decision by Carrier Corp., an air conditioning and furnace maker, to retain some jobs in the U.S. rather than relocate them to Mexico.

He said he was in the room when Mr. Trump made phone calls to company officials, describing his plans to make the economy friendlier to business, an argument he said proved persuasive.

Mr. Pence, in a private meeting with Greg Hayes, chief executive of United Technologies Corp. , the owner of Carrier, also offered the company $7 million in state tax incentives over the next 10 years to keep about a third of the 2,100 Indiana workers in the U.S.

United Technologies’ status as a major federal defense contractor also played a role in its decision to appease the incoming administration by not moving as many workers out of Indiana, people familiar with the deal said.

Mr. Trump chose to “speak as one American to another and tell them everything that we said we were going to do,” said Mr. Pence, including “cutting taxes on job creators and businesses, rolling back excessive regulations, repealing Obamacare and having the kind of trade deals that put Americans first.”

Write to Peter Nicholas at peter.nicholas@wsj.com