Perhaps less (or similar) lawmaking power, but the President of the US leads an entire branch of government which comes with a significant amount of power in its own right.
The President leads the Executive Office of the President. The Federal agencies (the Treasury Department, Department of Defense, ...) are themselves led by Cabinet Secretaries nominated by the President and confirmed by the Senate. The Prime Minister appoints Ministers not subject to confirmation by anyone else.
You are about to see how important this confirmation veto is.
