PARIS (Reuters) - U.S. Secretary of State Rex Tillerson on Friday questioned some of Saudi Arabia s recent moves in the Middle East, suggesting it should consider its actions more carefully, a rare rebuke when Washington s own policies in the region are under fire.   Publicly, U.S. President Donald Trump, his top aides and senior Saudi officials have hailed what they say is a major improvement in U.S.-Saudi ties compared with relations under former President Barack Obama, who upset the Saudis by sealing a nuclear deal with their arch-foe Iran. However, U.S. diplomats and intelligence analysts privately express anxiety over some of the more hawkish actions by Saudi Arabia s Crown Prince Mohammed bin Salman, especially towards Yemen, Qatar and Lebanon, as Saudi Arabia seeks to contain Iranian influence.  With respect to Saudi Arabia s engagement with Qatar, how they re handling the Yemen war that they re engaged in, the Lebanon situation, we would encourage them to be a bit more measured and a bit more thoughtful in those actions to, I think, fully consider the consequences,  Tillerson told a news conference alongside his French counterpart Jean-Yves Le Drian. In Yemen, Riyadh is leading an Arab military coalition against the Houthi movement that controls the capital. In recent weeks it imposed a blockade of ports, threatening to worsen what the United Nations says could become one of the worst famines in modern times. Saudi Arabia has also led neighboring Gulf Arab countries this year in cutting off trade and diplomatic ties with their neighbor Qatar, which Riyadh says supports terrorism. Qatar is an important American ally and home to a big U.S. air base. A month ago, the prime minister of Lebanon announced he was resigning while on a visit to Saudi Arabia. He returned home two weeks later and withdrew his resignation last week, drawing a line under the episode. Tillerson s comments were the latest sign of U.S. concern over aspects of the kingdom s foreign policy after Trump on Wednesday issued a one-paragraph statement demanding the Saudis allow immediate humanitarian aid to reach the Yemeni people. Although the blockade showed signs of breaking this week, Yemen s situation remains dire. About 8 million people are on the brink of famine with outbreaks of cholera and diphtheria.  We have called for a complete end of the blockade in Yemen and the opening of all ports. We are asking Saudi Arabia to allow that access,  Tillerson said. Tillerson s comments appear to be the first time the United States had publicly linked Saudi Arabia to the political crisis that broke out in Lebanon after Prime Minister Saad al-Hariri announced his resignation last month in Riyadh.  I think as to Lebanon, things have worked out in a very positive way,  Tillerson said.  Perhaps even more positive than before, because there have been very strong statements of affirmation for Lebanon, which will only be helpful.  Tillerson s rebuke comes at a time when Washington needs support from its major Arab ally, after Trump s decision to recognize Jerusalem as the capital of Israel earlier this week.  When asked whether there was room for Palestinians also to achieve their goal of having part of Jerusalem as their capital, Tillerson emphasized that Trump s move was not intended to shut down their demands over the city.  In fact, he was very clear, I think, the final status of Jerusalem, including the borders, would be left to the parties to negotiate and decide,  Tillerson said. 