Donald Trump has won presidential primaries in all five US states that voted on Tuesday, while Hillary Clinton took four out of five.
Mr Trump called himself the Republican “presumptive nominee” after victories in Connecticut, Delaware, Maryland, Pennsylvania and Rhode Island.
The results bring him closer to the number of delegates he needs before the party’s national convention in July.
For the Democrats, Mrs Clinton was denied a clean sweep by Bernie Sanders.
Mr Sanders won the vote in Rhode Island, and vowed to fight to the end of the primaries process.
Speaking at Philadelphia Convention Center after securing the four other states, Mrs Clinton said her campaign was setting “bold, progressive goals” to improve lives in the US.
“We believe in the goodness of our people and the greatness of our nation,” she said.
Meanwhile Mr Trump told supporters in New York he would not moderate his policies if elected president.
“I’m not changing,” he said. “You know I went to the best schools. I’m like a very smart person. I’m going to represent our country with dignity and very well.
“But I don’t really want to change my personality. You know, it got me here.”
Analysis: Anthony Zurcher, BBC North America reporter
There’s winning, and then there’s WINNING.
Donald Trump’s night is shaping up to be the latter, as he steamrolls his opposition in all five of mid-Atlantic states voting on Tuesday.
This campaign season has been punctuated with a series of theories about how and why Mr Trump’s presidential ambitions would eventually be thwarted. The latest was that he’d never be able to win more than 50% of the vote as the field narrows. It appears likely that he’ll easily surpass that mark across the board and claim the lion’s share of the delegates at stake.
During a primary night speech that took place before the polls even closed, Texas Senator Ted Cruz promised that his campaign was now heading to “more favourable terrain”. He’s setting up a firewall in Indiana, but there’s a Trump-fuelled conflagration heading his way.
The New Yorker still has work to do to clinch the Republican nomination, but after his latest performance such a prospect seems increasingly likely.
His rivals, Ted Cruz and John Kasich, have already shifted their attention to upcoming states, teaming up to help each other in the Indiana, Oregon and New Mexico primaries.
Mr Trump has condemned their pact as a sign of weakness and desperation, and another sign of the Republican party colluding against him. “The Republican party needs something much better than that,” he said after his latest victories were announced on Tuesday.
Neither Mr Kasich nor Mr Cruz has a chance of securing the Republican nomination outright. The hope of a contested convention this July in Cleveland is keeping them in the race.
This scenario would see party delegates – Republican officials and activists – choose the nominee. However Mr Trump is edging closer to securing 1,237 delegates, which would mean he could secure the nomination before the convention.
Speaking in Huntington, West Virginia, after the vote, Bernie Sanders vowed to fight to the end of the nomination process, saying he would attract broad support in November’s election.
“The reason that we are generating this enthusiasm is because we are doing something very unusual in contemporary politics. We are telling the truth,” he said.
Despite some success, it is unlikely Mr Sanders will be able to overcome Mrs Clinton’s lead to become the Democratic nominee for president.
The pact between Mr Kasich and Mr Cruz got off to a rocky start on Tuesday. The Ohio governor is to give Mr Cruz a “clear path” by not campaigning in Indiana and Mr Cruz will reciprocate in New Mexico and Oregon. But neither has endorsed tactical voting among their supporters.
Speaking in Indiana on Tuesday night, Mr Cruz said his supporters could look forward to some success as the race moved on to more conservative states.
His event was held at a basketball court where some scenes were filmed for the 1986 film Hoosiers, about a small-town high school basketball team that wins the state championship.
The Texas senator attempted to recreate a scene from the film but was mocked on social media for referring to a basketball “ring” rather than a “hoop”