Sheik Nawaf assumed power after the death last Tuesday of his brother Sheikh Sabah al-Ahmad. The late emir balanced his nation's ties between larger neighbors Saudi Arabia and Iran and kept a strong relationship with the United States, which led a coalition that ended Iraq's 1990-91 occupation of Kuwait.
"He will be remembered as a great man and a special friend to the United States," US Defence Secretary Mark Esper said in comments tweeted by the US Embassy during his visit.
Kuwait's state news agency said Sheikh Nawaf also received Iranian Foreign Minister Mohammad Javad Zarif, who had lauded the late emir for fostering "moderation and balance."
Sheik Nawaf, 83, is expected to uphold the OPEC member state's oil and foreign policy, which promoted regional detente.
He has yet to name a crown prince to help guide state affairs at a time when low crude prices and COVID-19 have hit state finances and amid tensions between foes Riyadh and Tehran.
The emir has up to a year to name an heir but analysts expect a decision in coming weeks as senior al-Sabah dynasty members jostle for position. Parliament must approve the choice.
"An appointment would end this competition and send a signal of stability," Dr. Mohamed Alfili, a professor of constitutional law at Kuwait University, told Reuters.
Among mooted candidates are Sheikh Nasser Sabah al-Ahmad, a former defense minister; Sheikh Nasser al-Mohammad, a former premier; and Sheikh Meshal al-Ahmad al-Jaber, deputy chief of the National Guard.
Another potential contender is Sheikh Mohammed Sabah al-Salem, a former foreign minister and the only candidate under discussion from the less powerful al-Salem family branch.
Kuwaiti sources say Meshal, the eldest among them, appears most likely to get the role.Saudi Arabi's de facto ruler Crown Prince Mohammed bin Salman called Sheikh Meshal on Saturday to offer his condolences, the Saudi state news agency reported.