Cork will take on Wexford in Round One of the All-Ireland hurling qualifiers following the live draw on RTÉ Radio 1's Morning Ireland.
The Rebels will face a testing trip to Wexford Park after the Model County suffered a heavy Leinster Championship defeat to Kilkenny at the weekend.
Dublin and Laois, who were also on the wrong end of big defeats in Leinster, will meet at Portlaoise. Limerick must now face a trip to Westmeath after their Munster championship defeat to Tipperary.
In the round's other tie Davy Fitzgerald's Clare will have home advantage over Offaly.
In Round 2A of the All-Ireland football qualifiers there's an all-Ulster affair as Antrim host local rivals Fermanagh.
Offaly will be waiting for the losers of Dublin v Kildare, while the Clare footballers have, like their hurling side, been handed a home tie - this one against Longford.
Cavan against Roscommon Roscommon complete the draw.
All-Ireland Round 1 hurling qualifiers
Saturday 4 July
1900 Laois v Dublin, O'Moore Park
1900 Clare v Offaly, Cusack Park
1900 Wexford v Cork, Innovate Wexford Park
Saturday 4 July/Sunday 5 July
TBC Westmeath v Limerick, Cusack Park
All-Ireland Round 2A football qualifiers
Saturday 4 July
1500 Offaly v Dublin/Kildare, O'Connor Park
1700 Cavan v Roscommon, Kingspan Breffni Park
1700 Clare v Longford, Cusack Park
Sunday 5 July
1500 Fermanagh v Antrim, Brewster Park
