Speaking at the World Economic Forum (WEF) in Davos, Switzerland on Sunday, Cheney called on his "democratic friends" to join the effort.
"Our forward strategy for freedom commits us to support those who work and sacrifice for reform across the greater Middle East. We call upon our democratic friends and allies everywhere, and in Europe in particular, to join us in this effort," he said.
The Bush administration believes a deficit in political and economic freedom in some Muslim countries is a key factor fuelling terrorism that poses a security threat to the West.
Officials say it plans to make President George Bush's "greater Middle East initiative" a centrepiece of transatlantic diplomacy this year.
"If they (Americans) want to produce democracy in the Middle East, they'd better do it first in Iraq as they promised."
Amr Musa, Secretary General
Arab and Muslim leaders in Davos voiced deep suspicion of attempts to impose democracy from outside, especially by the United States, which they accuse of double standards in its approach to the Israeli-Palestinian conflict, Iraq and Iran.
"If they (Americans) want to produce democracy in the Middle East, they'd better do it first in Iraq as they promised," Arab League Secretary General Amr Musa told Reuters.
Musa said he favoured democratic change, but suggested Arabs bristled when offered lessons in democracy by pro-Israeli right-wing ideologues associated with the Bush administration.
A senior member of Saudi Arabia's ruling family, Prince Turki bin Faisal, said it was hypocritical to preach democracy, but refuse to recognise the democratically elected leader of the Palestinian people, Yasir Arafat.
EU foreign policy chief Javier Solana, while welcoming the dialogue with Washington on the greater Middle East, cautioned against illusory grand structures that tried to tie together disparate problems under a single label.
"To think that from Morocco to Afghanistan we're going to have something which is structured is a bit of a chimera," Solana said. He noted that the EU already had agreements and cooperation with a dozen Mediterranean partners offering trade and aid in return for economic reform and human rights.
Solana said there was no clear US idea on the table yet, and added it would be hard to get the collective engagement of the Arab world for democratisation "without putting the same energy into the solution of the Palestinian-Israeli peace process".