The approvals came after Democrats said Republicans were holding up the nominations to undermine Obama's agenda in his final year in office.
Cruz placed a hold last year on all nominees for State Department positions requiring Senate confirmation, due in part to his opposition to the landmark nuclear deal Obama and other nations brokered with Iran.
Under Senate rules, a hold is a parliamentary procedure that allows a senator to block a nomination and other motions from coming to the floor for a vote.
Liu is a Chinese activist and Nobel Peace Prize winner imprisoned on charges of inciting state subversion. Novack said Cruz would continue to oppose the Iran nuclear deal.
The State Department nominees approved are Thomas A. Shannon Jr. To be undersecretary of state for political affairs and Brian Egan to be the department's legal adviser.
The US ambassadors approved today are Azita Raji, to be ambassador to Sweden; Samuel D. Heins, to be Ambassador to Norway; John L. Estrada, to be ambassador to Trinidad and Tobago; and David McKean, to be ambassador to Luxembourg. The Senate also confirmed Sunil Sabharwal to be alternate executive director of the International Monetary Fund.