Clinton said the attacks will only strengthen their resolve to stand together as allies and defeat terrorism and radical jihadism around the world.
The former Secretary of State said though terrorists have once again struck at the heart of Europe, but their campaign of hate and fear will not succeed.
"The people of Brussels, of Europe, and of the world will not be intimidated by these vicious killers. Today Americans stand in solidarity with our European allies," she said.
Trump, on the other hand, called for more vigilance.
"Do you all remember how beautiful and safe a place Brussels was? Not anymore, it is from a different world! US must be vigilant and smart!" he said in a tweet and criticised Obama in another tweet.
"President Obama looks and sounds so ridiculous making his speech in Cuba, especially in the shadows of Brussels. He is being treated badly!" Trump said.
"US officials have been and will continue to be in close contact with their Belgian counterparts," a White House official said.
The Ohio Governor John Kasich said "along with every American, he is sickened by the pictures of the carnage, by the injuries and by the loss of life."
"Today's attack is a brutal reminder that the international community must come together to destroy ISIS. This type of barbarism cannot be allowed to continue," said Senator Bernie sanders, the Democratic presidential candidate.
"The horrific attacks in Brussels were sadly predictable. And they are a reminder of what should by now be painfully obvious: the United States and Europe are at war with ISIL," Senators John McCain and Lindsey Graham said in a joint statement.
(Reopens FES114)
US Defence Secretary Ashton Carter said that the attacks reinforces the need to accelerate the defeat of Islamic State militant group that has claimed responsibility for carrying out the deadly attacks.
"The Brussels attacks reinforce our need to accelerate the defeat of ISIL. We have a strategy for doing so," Carter told lawmakers during a Congressional hearing convened by the House Armed Services Committee.
Carter was responding to a question from Congressman Mac Thornberry, Chairman of the House Armed Services Committee on how ISIS can be defeated in the wake of the terrorist attacks in Brussels.
"Brussels is an international city. It has been host to NATO and to the European Union for decades. Together, we must and we will continue to do everything we can to protect our homelands and defeat terrorists wherever they threaten us," Carter said.
Trump also called for closing of the American borders.
"We have to close our borders, make them so strong and let people into our country, but they have to be people that are going to be wonderful for our country," Trump was quoted as saying by the Fox News.
"I'm very strong on borders. I mean, I've been very, very strong from the beginning. I came out strong on trade, strong on borders and that was the initial and then you had the Paris attack and we started talking more in terms of military, also. But we have to strengthen up our borders a lot. And you know in the southern border, we're going to build a wall. We're going to absolutely build a wall," Trump said.
"We are having problems with the Muslims and we're having problems with Muslims coming into the country and we are seeing it, whether it's California where they killed the 14 people, the two young married couple, I guess she possibly radicalised him, nobody knows," he said.
