In the Platts window, Litasco returned to bid for 90,000 tonnes of CPC Blend at dated Brent minus $1.10 a barrel loading June 25-29, up from a $1.35 discount in Friday's session.
Algeria's state firm Sonatrach was offering Saharan Blend at around dated Brent minus 50 cents a barrel, several traders said, but adding that the grade was weaker with few deals taking place.
Vitol and BP were offering June cargoes of Saharan Blend. BP's cargo has already loaded.
Iraq's state marketer has allocated its July cargoes but a full programme had not yet emerged.
Exports of Kazakh CPC Blend crude oil are set to rise in July to 4.8 million tonnes from the revised June programme of 4.58 million tonnes, a programme showed on Monday.
The Urals swap was at $0.95 a barrel in the Mediterranean and $1.15 a barrel in northwest Europe.
Saudi Arabia, the world's top oil exporter, will limit volumes of crude to some Asian buyers in July and deepen cuts in allocations to the United States, industry sources with knowledge of the matter said on Monday.
OPEC's battle against an oil glut is under threat as unsold crude from members Nigeria and Libya, which are exempt from a global production-cutting deal, is swamping the Atlantic Basin.