The jet came down a few hundred metres (yards) short of the runway at Smolenk's Severny airport.
"It clipped the tops of the trees, crashed down and broke into pieces," Antufiev told Russia-24 television news network. "There were no survivors." Russian news agencies said pilot error was suspected.
The wreckage was scattered across a forest with parts of it still on fire, Russian television images showed. One of the black box flight recorders was quickly found, news agencies reported.
As well as killing the 60-year-old head of state, the crash devastated Poland's military leadership.
Former Polish president Lech Walesa, who headed the Solidarity movement, called the disaster "inconceivable".
"The Soviets killed Polish elites in Katyn 70 years ago. Today, the Polish elite died there while getting ready to pay homage to the Poles killed there," a shaken Walesa told AFP.
The 88 passengers included General Franciszek Gagor, chief of Poland's armed forces and the heads of all the main armed forces, central bank governor Slawomir Skrzypek, deputy foreign minister Andrzej Kremer, Kaczynski's wife Maria, and scores of MPs, historians and other officials.
Bronislaw Komorowski, head of Poland's lower house, was to take over as interim head-of-state. Poland's remaining military leaders called a crisis meeting while the country was to hold a week of official mourning.
The delegation was to attend a memorial service in the Katyn Forest, near the crash scene, where 22,000 top Polish officers and troops were killed by Soviet troops 70 years ago. The event had been intended to help reconciliation between Poland and Russia.
The jet's engines and a large chunk of its mud-caked tailfin was strewn over a large area in the fog-blanketed forest.
Firefighters hosed down burning sections of the plane while security personnel and civilian investigators inspected the wreckage.
Russian news agencies reported that pilot error was suspected. "The cause of the plane crash was apparently an error by the crew during the approach to landing," Russian state news agency RIA Novosti quoted an unnamed official in Smolensk as saying.
Russian President Dmitry Medvedev appointed Prime Minister Vladimir Putin to head an inquiry commission and sent Emergency Situations Minister Sergei Shoigu to the site.
Kaczynski was the identical twin brother of former prime minister Jaroslaw with whom he led Poland's nationalist right wing, stubbornly taking on other European leaders at EU summits to defend his country's cause.
He faced an election later this year but was to fight for a new term.
Kaczynski was to lead the Polish delegation at commemorative ceremonies for the Katyn massacre, which decimated Poland's military and intellectual elite 70 years ago.
The crash occurred three days after Putin and his Polish counterpart, Donald Tusk, together attended a memorial for the victims of the massacre at Katyn.
The Putin-Tusk meeting there was seen as a huge symbolic advance in Russia's often thorny relations with Poland.
Putin called Polish Prime Minister Donald Tusk to express condolences over the "tragic" crash, the Russian leader's spokesman Dmitry Peskov told Russian news agencies.
"I have given an order to carry out a detailed investigation of the accident with complete and close cooperation with the Polish side," Medvedev said in a message to Bronislaw Komorowski, head of the Polish parliament who is set to take over Kascynski's duties.
"Russia shares Poland's grief and mourning. I ask you to offer my sincerest condolences to the Polish people, words of sympathy and support for the relatives and loved ones of the dead," said the message, posted on the Kremlin website.
World leaders expressed shock at the disaster.
French President Nicholas Sarkozy said he "conveys all his sympathy to the family of president Kaczynski and to the families of all the victims and wishes to express his deep personal condolences and on behalf of the French people."
He paid homage to his Polish counterpart as a man "driven by ardent patriotism, who dedicated his life to his country."
German Chancellor Angela Merkel said: "I am deeply shocked by the plane accident and the death of the Polish president."
"He will be mourned across the world and remembered as a passionate patriot and democrat," said British Prime Minister Gordon Brown.