Mourners lined the route taken by first lady Maria Kaczynska's hearse
US President Barack Obama will attend the funeral of his Polish counterpart Lech Kaczynski, killed in an air crash in western Russia on Saturday.
The leaders of Russia, France and Germany are also due to attend the burial in the city of Krakow on Sunday.
Mr Kaczynski and his wife Maria will be buried in a crypt close to iconic Polish leader Jozef Pilsudski - a decision that has aroused some protest.
Polish officials say elections for a new president will be held in June.
In a parliamentary document they wrote that there were "two possible dates" for the election - 13 or 20 June.
Poland's acting President, Bronislaw Komorowski, is expected to name the exact date after consulting political parties.
Before the crash, Mr Komorowski, the parliamentary speaker, was expected to run against the late president as the official candidate of Prime Minister Donald Tusk's governing Civic Platform Party.
There is speculation that Jaroslaw Kaczynski, twin brother of Lech Kaczynski, may now stand in the late president's place.
The bodies of the presidential couple have been lying in state together at the presidential palace in Warsaw since the remains of the first lady arrived from Moscow on Tuesday, a few days after her husband's repatriation.
The coffins of Poland's first couple are lying in state in Warsaw
A Polish air force band greeted her coffin as it arrived back in Warsaw. Covered in a white and red Polish flag, the coffin was met by the president and the first lady's daughter, Marta, who kneeled down to touch it.
Andre Ladinski, a political commentator, told the BBC that while President Kaczynski was a divisive politician, the first lady was universally admired.
"She was very much liked, loved by people, people really warmed up to her, I would say that not many politicians' wives were so popular as she was," he said.
The couple were among 96 people - many of them senior figures - aboard a Polish government jet that crashed in heavy fog while trying to land in the Smolensk region of Russia.
They had been travelling to attend a memorial service for Polish military officers and others killed en masse by Stalin's secret police at Katyn in 1940.
Polish TV has been broadcasting live images of mourners walking by the closed coffins of the first couple at the presidential palace.
Krakow's Archbishop, Stanislaw Dziwisz, announced that the funeral would begin at 1400 (1200 GMT) on Sunday in the city's medieval Wawel Cathedral, the main burial site of Polish monarchs since the 14th Century and more recent heroes including Josef Pilsudski, who led Poland after independence from Russia in the early part of the last century.
The last Polish leader killed in office, Gen Wladyslaw Sikorski, who died in an air crash in 1943, is also interred there.
Some Poles criticised the decision to bury Mr Kaczynski, who was a divisive political figure in his lifetime, in the cathedral.
Hundreds of people staged a protest in front of the archbishop's residence on Tuesday evening, carrying banners reading: "Not Krakow, not Wawel", and "Are you sure he is the equal of kings?"
Other victims of the crash, whose bodies are believed to have been badly disfigured or burnt in the crash, are being identified by forensic scientists in Moscow. A number of the dead have yet to be retrieved from the wreckage of the plane in the Smolensk region.
The wreckage of the jet is still being searched for bodies
Polish Prosecutor General Andrzej Seremet said on Tuesday that 87 bodies had been recovered and 40 of them identified.
A source in the team set up in Moscow to help the relatives of the dead, who are in the city to identify their loved ones, later told Russian news agency Interfax that 62 bodies had been identified.
Thirty of the bodies are due to be repatriated on Wednesday, the source added.
Russian investigators believe pilot error was to blame for the crash.
The Soviet-built Tu-154 jet's flight recorders have been recovered and data from them is due to be analysed jointly by investigators from both countries.
Russian air traffic controllers who handled the plane have been quoted as saying the Polish crew refused three times to heed advice to divert to another airport.
"The crew did not listen, although the controllers warned them about bad visibility and told them to get ready to fly to a reserve airport," Anatoly Muravyov, one of the controllers who handled the plane, told Russia's Komsomolskaya Pravda newspaper.
There has been speculation in Poland and elsewhere that the plane's pilots may have felt under pressure to land without delay, in order for their passengers to attend the Katyn memorial service on time.
The plane finally hit treetops on its fourth attempt to land.