Tusk said the president's campaign had 'brought shame on Poland from around the world'.
He will face a run-off vote in two weeks' time against Warsaw mayor Rafal Trzaskowski, who is standing for the largest opposition party, the centrist Civic Platform (PO).
For Mr Trzaskowski, the problem is the conservatives' tight grip on power. "There was a candidate of the leftist party, for example, so [.] who will the voters of a leftist party support in the second round?"
The turnout in the election was 64.4 per cent, despite the coronavirus pandemic meaning that many people had to wait in socially distanced lines outside polling stations.
Last week, Mr Duda travelled to Washington and received a ringing endorsement from President Donald Trump.
While PiS insists the changes are needed to weed out judicial corruption, critics and the European Union insist they erode judicial independence and democracy just three decades after Poland shed communism.
Experts were divided on who could win the election next month.
"The campaign goes on because Poland needs it", Duda told jubilant supporters in the central town of Lowicz. He also thanked his election rivals and said Trzaskowski had a good chance to run against him in a second round. The final result will not be declared until July 1, but with nearly 90 per cent of votes counted, Mr Duda had received more than 45 per cent of the vote, well ahead of his main rival Rafał Trzaskowski, the mayor of Warsaw, on 29 per cent.
'This is a decisive time. "A lot will really depend on this decision", said Poland's anti-communist hero Lech Walesa as he voted in the northern port of Gdansk.
A left-wing politician who was Poland's first openly gay presidential candidate, Robert Biedron, was expected to win 2.9 percent, while an agrarian candidate, Wladyslaw Kosiak-Kamysz, had 2.6 percent in the poll. output.
That kind of rhetoric, along with judicial review and the party's use of public media to promote the government's image, has raised concern among some that Poland is following Hungary in the erosion of democratic norms established after the collapse of communism three decades ago.
Some analysts view the election as a crucial juncture: a second five-year term for Duda would allow the PiS to make even more controversial changes while defeat could unravel the party's power. For democracy, the judiciary and respect for minorities, ' said Joanna Ugniewska, 66, after casting her ballot at a polling station in a school in Warsaw city centre.
But in Tarnow in southern Poland, a stronghold for the PiS, Andrzej Guzik said he would be voting for Duda because of his consistent leadership. "I will be the candidate for change", he said.
Poland's government has implemented popular social welfare payments in recent years but has also endorsed polarizing legislation, especially judicial reforms.
The election was scheduled to be held in May but had to be postponed because of the virus outbreak.
He likened "LGBT ideology" to a new form of communism.
Mr Trzaskowski's programme calls for allowing same-sex civil partnerships but not marriage, and he has largely avoided the issue on the campaign trail.
Campaigning with the slogan "Enough is Enough", Trzaskowski promises to use the experience and contacts he gathered as a former European affairs minister to "fight hard" for a fair slice of the EU's 2021-27 budget, and to fix tattered ties with Brussels.