Eleven year olds take national tests at the end of primary school
Parents want their children to sit tests at the age of 11, the chief inspector of schools in England says.
Parents needed "some clarity" about how their children were doing before they started at secondary school, Christine Gilbert told a committee of MPs.
Ms Gilbert said she was relaxed about the scrapping of tests for 14 year olds, but not for Key Stage 2 pupils.
She also stressed the need for school report cards, being introduced by the government, to be clear and simple.
Giving evidence to the cross-party schools committee on Wednesday, Ms Gilbert said KS2 results marked the end of an important phase of education.
"It would be difficult if there were no Sats results, but it would depend on what replaces them," she told MPs.
Key Stage 3 tests for 14 year olds were scrapped by the Schools Secretary, Ed Balls, last October.
Ms Gilbert said she had been "very relaxed" about this move, but added: "I'm not so relaxed about the removal of KS2.
"There seems to be a number of debates about what would replace them. It would be very serious for us."
Ms Gilbert was also asked about the aim of the proposed school report card.
The measure is used in the United States to measure pupils' achievement and well-being and is being planned by Mr Balls for use in schools in England.
"I see it as primarily aimed at parents, the public and pupils themselves," Ms Gilbert said.
School report cards are likely to be a Labour pledge at the election
"I do think it's important... that at first glance it has a real sharpness and a clarity and gives a clear picture of the school.
"One of the things I would hope for is some simplicity."
Ms Gilbert said parents told her they were often overwhelmed by the different information on schools available to them.
Asked who would be responsible for writing the report cards, Ms Gilbert said she could not say, but assumed the Department for Children, Schools and Families (DCSF) would write the cards.
Her response prompted criticism from Labour MP David Chaytor, who said Ofsted should seek to keep control of the grading of schools.
Earlier she stressed the importance of the watchdog remaining free from government control.
"If we lost our independence, we'd lose our integrity. I really would guard its [Ofsted's] independence."
There were criticisms in Ofsted's annual report - for example that the number of children moving from primary to secondary school who cannot read was "unacceptable" - which could not be made if the organisation were a government outpost, she added.
Ms Gilbert denied the watchdog was overwhelmed now that it had taken on responsibility for inspecting children's services and stressed school inspections remained a core part of its work.
She said inspectors were currently trialling no-notice inspections for schools - 17 were carried out last term.
"Head teachers that have experienced it have been positive about it in general," she said.
But parents and governors had been less impressed, as they were often not aware inspectors were in school.
Asked about the role of self-evaluation in inspections, Ms Gilbert said the process was useful for schools.
She said the form head teachers currently filled in as part of their self-evaluation was being shortened in response to heads' concerns.
"We are just about to put the draft of it on the website," she added.