West Ham will face FC Astra Giurgiu or Romania in the Europa League third qualifying round after surviving penalties in Malta on Thursday.
The Premier League side played with 10 men for over an hour against Birkirkara after James Tomkins was sent off, and will resume their campaign at home next Thursday.
FC Astra advanced after a goalless draw with Inverness, going through 1-0 on aggregate.
Aberdeen are the only Scottish team remaining and will face Kairat Almaty of Kazakstan in the third round after seeing off Rijeka on Thursday,
Southampton enter the competition at this stage and will face Dutch club Vitesse Arnhem.
The fixture will see Southampton manager Ronald Koeman return to the Netherlands, where he previously managed Vitesse before moving to England.
In other notable ties, Borussia Dortmund will face Austrian side Wolfsberger AC, and Athletic Bilbao will face Azerbaijan's Inter Baku.
Third qualifying round: Ties to be played July 30 and Aug. 6: