Larijani and Solana last met in Ankara April 25-26 and there was some progress made at the talks in finding common ground on some issues.
Larijani said upon his arrival that "Tehran is ready for other countries, for example France, to join talks on the Iranian nuclear dossier."
He added that he did not intend to meet with U.S. Secretary of State Condoleezza Rice, who is expected to arrive in Madrid Friday.
Iran failed to comply with a 60-day deadline to stop uranium enrichment imposed by the UN Security Council and has increased uranium enrichment, saying its nuclear program is aimed exclusively at power generation.
Secretary General of the International Atomic Energy Agency (IAEA) Mohamed ElBaradei said last week it was too late to force Tehran to abandon its uranium enrichment plans and proposed introducing inspection measures instead to prevent a further expansion of the Iranian nuclear program.
The United States has threatened Iran with further sanctions.
