Putin spent Sunday in Saudi Arabia and will remain there on Monday before travelling to Qatar and Jordan.
The visit is the first by a Russian president to the countries and will follow Putin's landmark Middle East visit in 2005, to Israel, Egypt and the Palestinian territories.
'Man of peace'
Abdullah described the Russian leader as "a statesman, a man of peace, a man of justice."
Putin said he was as a "loyal friend" of the Muslim kingdom and said the two countries could do much to bolster ties.
The two leaders oversaw the signing of a series of economic, cultural and information agreements between the countries.
The trip is a notable step for Russia towards Middle East states closely allied with the US, since Moscow has traditionally had closer ties with Syria and Iran, who Washington regard as state sponsors of terrorism.
Putin said on Saturday he failed to understand why Iran had not answered all the IAEA's questions.
"We expect Moscow to do its best to prevent the adoption of another resolution against Iran"
Ali Akbar Velayati, senior adviser to Ayatollah Ali Khamenei
"I don't quite understand why Iran has not responded fully and constructively to [IAEA chief Mohamed] El Baradei's questions and concerns," he said.
On Sunday, Iran said it wants Russia to prevent the UN security council from adopting any new resolution against the Islamic republic when a deadline runs out for it to halt controversial nuclear work.
Ali Akbar Velayati, a senior adviser to Ayatollah Ali Khamenei, Iran's supreme leader, said: "We expect Moscow to do its best to prevent the adoption of another resolution against Iran."
"We are aware of their limitations but our expectations stand," he said.
Russia, a permanent Security Council member, is a close partner of Iran and is building the country's first nuclear power station, as well as supplying sophisticated defence technology.
Questions over Russia's stance on Iran will likely be raised during the Russian president's Middle East visit.
The US, the EU and other countries fear that Iran is developing nuclear weapons under cover of a civilian atomic energy programme. Tehran denies this, insisting it is pursuing peaceful power generation and not bombs.
The IAEA has repeatedly urged Iran to answer questions about its uranium enrichment programme and other activities it hid from UN inspectors for nearly two decades until 2003.