President Lech Kaczynski was scheduled to attend a ceremony in nearby Katyn to commemorate the 20,000 Polish officers killed by Soviet secret police during World War II, RIA Novosti said.
The report said the Soviet-made Tu-154 hit trees as it neared Smolensk in the fog.
Polish Prime Minister Donald Tusk and Russian Prime Minister Vladimir Putin were on their way to the crash site, the Russian news agency said.
Acting President and parliamentary Speaker Bronislaw Komorowski said, "I have just signed a decision on the announcement of a national week of mourning."
In Washington, U.S. President Barack Obama offered his condolences.
"Today's loss is devastating to Poland, to the United States, and to the world," Obama said in a statement. "President Kaczynski was a distinguished statesman who played a key role in the Solidarity movement, and he was widely admired in the United States as a leader dedicated to advancing freedom and human dignity. With him were many of Poland's most distinguished civilian and military leaders who have helped to shape Poland's inspiring democratic transformation."