Washington, June 12 (Reuters): Donald Trump, the presumptive Republican presidential candidate, wasted little time to suggest that the Orlando attack was tied to Islamist militants, while his Democratic rival Hillary Clinton initially did not make that connection.

Trump boasted on Twitter that he was "right on radical Islamic terrorism" and called for toughness and vigilance in the wake of the deadliest shooting in US history.

"Appreciate the congrats for being right on radical Islamic terrorism, I don't want congrats, I want toughness & vigilance," Trump tweeted after the Orlando shooting. "We must be smart."

As President Barack Obama on Sunday addressed the US about the massacre, Trump assailed him for his longstanding refusal to refer to the Islamic State and other extremist groups as in part representing the religion of Islam.

"Is President Obama going to finally mention the words radical Islamic terrorism?" Trump tweeted as the President was speaking. "If he doesn't, he should immediately resign in disgrace."

Trump in a later tweet claimed the gunman shouted "Allah hu Akbar!" during the attack. US officials as yet have not provided any information that such an incident occurred.

During the campaign for the November 8 presidential election, Trump has proposed a temporary ban on Muslims entering the US as a means to combat the threat of militant attacks.

An FBI official said the Orlando suspect might have had leanings towards the Islamic State's ideology but cautioned that the suspected connection required further investigation.

In his remarks at the White House, Obama said the investigation into the shootings was ongoing and declined to speculate on the motives of the shooter.

"We've reached no definitive judgement on the precise motivations of the killer," Obama said. "The FBI is appropriately investigating this as an act of terrorism."

Similarly, Clinton, in a statement, called the attack an "act of terror" but did not speculate as to the ideology of the gunman.

"Law enforcement and intelligence agencies are hard at work, and we will learn more in the hours and days ahead," said Clinton, the likely Democratic presidential nominee.

The office of Texas lieutenant governor Dan Patrick, a Republican and evangelical Christian, deleted a tweet many saw as offensive and insensitive that was sent out shortly after the deadly attack on a gay nightclub in Florida.

"Do not be deceived: God cannot be mocked. A man reaps what he sows," read the Bible verse Patrick sent out on his official Twitter account a few hours after the Orlando shooting. His office said the tweet had been scheduled for release well before the shooting.

Although the Islamic State claimed responsibility for the Orlando massacre, US officials said they had seen no immediate direct evidence linking the militant group to the nightclub attack.

The officials, who spoke on condition of anonymity, also said they had yet to see any direct contacts between any extremist group and the suspect.

The officials said a leading theory was that the suspect somehow was inspired by Islamic militants.

One official said early information, the nature of which he did not disclose, indicated that the shooter was motivated by a mixture of "hate" and religion.

US Representative Adam Schiff of California, the senior Democrat on the House Intelligence Committee, said in a statement issued after a briefing on the massacre that several factors indicated the attack was an Islamic State-inspired "act of terrorism".

He noted that the incident occurred during the holy month of Ramazan, that the Islamic State had called for attacks during that period, the target was an LGBT nightclub and it was hit during Gay Pride weekend.

Moreover, he said, that if accurate, "according to local law enforcement the shooter declared his allegiance to ISIS (Islamic State)."

An audio message purportedly issued last month by the spokesman for the Islamic State called on followers to launch attacks in the US and Europe during Ramazan, which began on June 5 in America.