Some 150,000 grieving Poles flooded the city for the burial of Kaczynski and his wife alongside past kings and heroes, although Europe's air travel chaos kept many world leaders away.
US President Barack Obama and dozens of other dignitaries were forced to abandon plans to attend because of the volcanic ash cloud.
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But Russian counterpart Dmitry Medvedev arrived to show solidarity after the April 10 plane crash in Russia that killed the couple and 94 others.
Tearful mourners applauded the Kaczynskis, tossed flowers and waved red and white flags as the cortege weaved through the narrow streets of Poland's former royal capital, after their bodies were flown by military aircraft from Warsaw.
Flag, flower tributes
Sirens wailed to mark the start of the funeral mass at the Gothic Basilica of Our Lady in Krakow's central square, where huge crowds had gathered to see the service relayed live on giant screens on Sunday.
The archbishop of Krakow, Stanislaw Dziwisz, thanked the foreign leaders who came to the service and said he hoped the crash would help end decades of tensions between Russia and Poland.
"The empathy and help that we experienced during these days from our Russian brothers raises hope for rapprochement and reconciliation," he said.
"These words I direct to Mr Medvedev, president of Russia."
Kaczynski's Tupolev Tu-154 jet slammed into a forest near Smolensk in western Russia while heading for a ceremony marking the 70th anniversary of the massacre of thousands of Polish officers by Soviet forces in the Katyn forest.
National outpouring of grief
Acting Polish president Bronislaw Komorowski - who met Medvedev before the funeral along with Polish Prime Minister Donald Tusk - said at the service he hoped Russia would one day reveal the full truth about the atrocity.
Despite his reputation as an often divisive nationalist, Kaczynski and his wife Maria were later to be laid to rest in the cathedral crypt of Krakow's Wawel castle, alongside Poland's monarchs, national heroes, saints and poets.
Their coffins were slowly taken on gun carriages to Wawel from the church by a procession of priests and soldiers.
The couple will then be lowered into a sarcophagus inscribed with their names and a cross. It will lie next to that of Poland's revered independence leader, Jozef Pilsudski.
The funeral marks the climax of a national outpouring of grief since the crash, which also killed scores of senior military and civilian officials.
Ash cloud disruption
"It's an exceptional moment. Poles have to be here," said Maria Kurowska, the mayor of the town of Jaslo, who was in the crowd.
Police said there were nearly 150,000 mourners in Krakow.
But the Icelandic volcano eruption that has disrupted European air travel also cast its shadow over the funeral.
German Chancellor Angela Merkel, French President Nicolas Sarkozy, Britain's Prince Charles and South Korean Prime Minister Chung Un-Chan were among dozens of dignitaries who cancelled.
The leaders of many countries close to Poland, including the Czech Republic, Estonia, Hungary, Lithuania, Romania, Slovakia and Slovenia, arrived in Krakow by road and rail instead.
