Adnani also announced an amnesty for people who fought against IS in Iraq's Anbar province, and called on residents who had fled violence there to return home.
"The best acts that bring you closer to God are jihad, so hurry to it and make sure to carry out the invasion this holy month and be exposed to martyrdom in it," Adnani said in an audio message posted online.
"These are your weapons and this is Ramadan."
Ramadan, which began last week, is the holy month in the Muslim calendar during which believers observe a fast from dawn to sunset every day.
Adnani repeated a call by IS chief Abu Bakr al-Baghdadi for those who fled Anbar, where IS seized provincial capital Ramadi last month, to return.
View galleryAn image grab taken from a propaganda video released …
An image grab taken from a propaganda video released on July 5, 2014 by al-Furqan Media allegedly sh …
"Oh people of Anbar, return to your homes and go back to your people," he said.
According to the International Organization for Migration, more than 275,000 people fled the Ramadi area between April and mid-June.
Adnani also announced a "last chance" for tribesmen, soldiers and police, calling on them to "repent" and surrender their weapons as a sign of good faith.
He singled out the Jughaifa tribe that is besieged in the town of Haditha, saying it faces utter destruction if it does not surrender.
If they do not "repent", then "for generations those passing Haditha will say: 'The Jughaifa were here, and their houses'."
As IS has previously executed hundreds of security personnel and tribesmen who opposed the group, it is unlikely that many will take up the offer.
IS launched a brutally effective offensive last June that overran large areas north and west of Baghdad.
Iraqi forces have made major gains in Diyala and Salaheddin provinces north of Baghdad, but much of the country's west is still in IS hands.
Posted by Women Against Shariah on Wednesday, June 24, 2015
From the AFP via Yahoo! News: