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The Kurdish regional government has reached four new oil-exploration deals, further straining relations with many Iraqi leaders in Baghdad.

The new deals are the latest in an effort by the Kurds to build their own oil industry while national oil legislation languishes in parliament. A similar agreement reached last month with the Hunt Oil Co. of Dallas was criticized as illegal by Iraq’s oil minister.

Kurdish officials say the deals are consistent with the Iraqi Constitution.

The new contracts were signed with Heritage Oil Corp., a Canadian concern, and Perenco S.A., a privately held French company. Two other deals with “experienced international companies” are to be announced soon. The total initial amount invested is expected to be $500 million, the regional government said.

Many Iraqi legislators object to the Kurdish interpretation of the constitution, and it is unclear how the Kurds’ own regional oil law, passed in August, will conform with whatever might ultimately be approved by the central government.