The PSNI confirmed the attack, involving a suspected improvised explosive device, happened in the Mount Carmel Heights area of the Co Tyrone town and a security operation is now underway.
Police remained at the scene on Friday morning after what was described as a “loud bang” was heard in the area when the attack happened after 11pm.
DUP West Tyrone MLA Tom Buchanan confirmed he has spoken with police in the area and said his “thoughts are with them”.
"I condemn this murderous incident. I am glad the police officers have survived this attempt to take life,” he said.
“I grew up with daily news reports of police officers being murdered. It was wrong then and it is wrong today.
"Police officers have always stood on the front line to protect people and serve their community. There has never been any justification for the murder of police officers.”
Ulster Unionist councillor Derek Hussey condemned the attack and said it was “the work of cowards and thugs”.
“Any support they have is miniscule, because the people of Strabane and the rest of Northern Ireland have repeatedly shown that they want nothing to do with this type of madness,” he said.
“Violence will not create a single job, heat a single home or give a single child a better future.
"All the people responsible have done is disrupt the local community - with 1,000 residents affected - and prevent people from going about their daily business.
"They have also ensured that children are unable to go to school this morning. And somehow the people responsible would claim they are striking a blow for Irish freedom.
"They are utterly deluded and living in a fantasy world, whilst the rest of us simply want to get on with our lives and our neighbours in peace.
“I urge anyone who can assist the police in any way to catch the people responsible to come forward with any information they have. Those who use violence to achieve political ends are fascists pure and simple. They have no place in this society and need to be put out of business permanently.”
SDLP leader Colum Eastwood said: “Lives put in danger, and children’s learning disrupted- for what?
“What is this achieving?”
The Police Federation of Northern Ireland – the body which represents rank-and-file officers across the province – described the attack as a “desperate, reckless act”.
“The terrorist goal was to cause heartache and misery and return Northern Ireland to the dark ages,” said chair Liam Kelly.
“We are grateful that officers in the vehicle targeted by these cowards were unhurt. The attackers wanted their roadside device to cause maximum damage and we are thankful they failed in their objective.
“This attack is a reminder to us all that terrorists are still active in our community. They want to maim or murder our men and women. The truth is they are a bankrupt throwback to another time and have nothing to offer society.
“I would appeal to people to help the police track down those responsible and bring them before the Courts."
Alliance Party councillor Stephen Donnelly said his thoughts were with the officers targeted.
"We could very easily be standing here today talking about the death of police officers. Nobody should face this kind of threat when simply doing their job,” he added.
West Tyrone MLA Daniel McCrossan said the incident has caused a “major inconvenience” for around 1,000 residents living in the area, including for children unable to go to school.
“More than 1000 people living in Mount Carmel Heights are experiencing immense disruption this morning as police investigate a security alert in the area,” he said.
"This is one of Strabane’s biggest residential areas and there is currently no way in or out as the scene is cordoned off.
“Local people have reported hearing a loud bang late last night which police are now investigating. This disruption means that nurses teachers and other public service workers are unable to get to work this morning.
“I am continuing to speak directly with the local PSNI and would urge people to co-operate with police so that we can secure the area and have the cordon lifted as soon as possible.”
The road is closed to motorists and drivers have been advised to avoid the area and seek alternative routes.
Police confirmed no homes have been evacuated at present.
A PSNI spokesperson said: “The Police Service can confirm that the ongoing security alert in the Mount Carmel Heights area of Strabane this morning, Friday 18th November follows what appears to have been a targeted attack on police shortly before 11pm last night.
“Investigations are at an early stage however the attack, which is believed to have been caused by an improvised explosive device, caused damage to a police vehicle and is being treated as the attempted murder of two officers.
“The road remains closed and motorists are advised to avoid the area. No homes have been evacuated at this time.
“A further update will be provided in due course.”