Donald Tusk, Poland's prime minister, said his government had received "unofficial confirmation" that Stancza had been killed.
"We have used every opportunity to avert this," he said in remarks broadcast live on Polish television.
Piotr Adamkiewicz, a spokesman for the Polish embassy in Islamabad, said that the information had come from a number of different sources and was considered to be "99.99 per cent true".
Abdul Basit, a spokesman for Pakistan's foreign ministry, said authorities were still "trying to ascertain the factual position".
Stancza was kidnapped on September 28 while visiting a site operated by Geofizyka Krakow, a Polish geophysics institute which he worked for, near Attock city, about 65km west of the capital, Islamabad.
Armed men shot dead his Pakistani driver, bodyguard and translator before taking him hostage.
The captors originally demanded that 60 of their group be freed, but cut their demands as negotiations intensified over the past 10 days.
The Taliban spokesman said Stanza was executed in the South Waziristan tribal region.
Attacks on foreign aid workers, company employees and diplomats have increased in Pakistan over the past year, especially in areas near the border with Afghanistan, where pro-Taliban fighters are battling government forces.
Last week, an US citizen heading the United Nations High Commission for Refugees (UNHCR) office in the southwestern province of Baluchistan, was abducted and his driver was shot dead.
On Saturday, a previously unknown group, calling itself the Baluchistan Liberation United Front, claimed it had seized the UN official and warned it would kill him if their demands were not met.
"We have three demands, and if our demands are not met, then John Solecki will lose his life," a spokesman, identifying himself as Shahak Baluch, told the Online news agency.
"We want the United Nations to secure the release of 141 women in Pakistani torture cells, provide information about more than 6,000 missing persons, and resolve the issue of Baluch independence under the Geneva Convention."
Separatist and national fighters have been fighting for greater political and economic autonomy for the southwestern province for decades.