Donald Trump has won presidential primaries in all five US states that voted on Tuesday, while Hillary Clinton triumphed in 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.
The Vermont senator won in Rhode Island and vowed to fight to the end of the primaries process.
Speaking at the 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.
After his sweep of the five states, Mr Trump said of the battle for the Republican nomination: “It’s over. As far as I’m concerned, it’s over.”
He told supporters in New York he would not moderate his policies if elected president.
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 steamrolled his opposition in all five mid-Atlantic states.
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.
Trump and Clinton deliver decisive blows
After their victories, Mr Trump and Mrs Clinton turned their fire on each other.
Mr Trump said his Democratic rival’s only advantage in the presidential race was being a woman.
“Frankly, if Hillary Clinton were a man, I don’t think she’d get 5% of the vote,” he said.
Mrs Clinton hit back at his accusation that she was playing the “woman card”.
“Well, if fighting for women’s healthcare and paid family leave and equal pay is playing the woman card, then deal me in,” she told cheering supporters in Philadelphia.
Mr Trump’s rivals, Ted Cruz and John Kasich, have already shifted their attention to forthcoming states.
As part of a new campaigning pact, Mr Kasich will give Mr Cruz a “clear path” to tackle Mr Trump in Indiana on Tuesday, with Mr Cruz reciprocating for Mr Kasich in the 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.
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.
Analysts believe that Indiana, with its 57 delegates, will be crucial if Mr Trump’s rivals are to stop him securing the 1,237 he needs to win outright.
Opinion polls suggest Mr Trump has 39% support there, Mr Cruz 33% and Mr Kasich 19%.
Mr Cruz told supporters in Indiana on Tuesday night they could look forward to some success as the race moved 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”.
Meanwhile, 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.
But he admitted to Associated Press he had a “very narrow path and we’re going to have to win some big victories”.