She said: " On Friday, following the attack in Nice, the police and the security and intelligence agencies took steps to review our own security measures and ensure that we have robust procedures in place, and I am receiving regular updates."
All police forces have reviewed upcoming events taking place in their regions to ensure security measures are " appropriate and proportionate", Ms Rudd told the Commons.
Eighty-four people were killed when Mohamed Lahouaiej Bouhlel drove a hired lorry through crowds gathered to celebrate Bastille Day on Thursday.
Ms Rudd said the UK has "considerable experience" in managing and policing major events.
Extra security measures used at particularly high-profile events include the deployment of measures known as the National Barrier Asset when police assess there to be a risk of vehicle attacks.
This is made up of a range of temporary equipment, including security fences and gates, that enable the physical protection of sites, the Home Secretary said.
Since the Mumbai attacks in 2008, steps have been taken to improve the response of police firearms teams and other emergency services to a marauding gun attack, Ms Rudd said, adding that counter-terrorism police funding had been protected and increased in real-terms.
She went on:"We continue to test our response to terrorist attacks, including learning the lessons from attacks like those we have seen in France, through national exercises which involve the Government, military, police, ambulance, fire and rescue service, and other agencies.
"But the threat from terrorism is serious and growing."
She said that the public should be "vigilant, but not alarmed".
Ms Rudd said Daesh - also known as Islamic State - and other terrorist organisations "seek to poison people's minds" and they "peddle sickening hate and lies to encourage people to plot acts of terrorism or leave their families to join them".
She said: "This is not just in France, or this country, but in countries all around the world. We must confront this hateful propaganda and expose it for what it is."
Ms Rudd - appointed as Home Secretary last week - said the full horror of the atrocity in Nice "defies all comprehension".
She said: "These were innocent people enjoying national celebrations. They were families - mothers, fathers, brothers, sisters, daughters and sons, and friends. Many of them were children.
"They were attacked in the most brutal and cowardly way possible, as they simply went about their lives."
Britain has offered "investigative assistance" to the French authorities, Ms Rudd told MPs, while she vowed that the UK will stand with France in the fight against terrorism.
" Nice was attacked on Bastille Day - itself a French symbol of liberation and national unity. Those who attack seek to divide us and spread hatred," she said.
"So our resounding response must be one of ever greater unity. Between different nations, but also between ourselves."
She concluded her statement with a message to " our French friends and neighbours".
Ms Rudd said: " What happened in Nice last Thursday was cruel and incomprehensible. The horror and devastation is something many people will live with for the rest of their lives.
"We know you are hurting. We know this will cause lasting pain. So let me be quite clear: We will stand with you. We will support you in this fight.
"And together, with our partners around the world, we will defeat those who seek to attack our way of life."