The Lubavitch Boys' Primary School in north London has been told that it must do better after its first inspection since becoming state-aided in 2012.
Ofsted, which visited last month, said that the school overall "requires improvement" because the "quality of teaching is not yet good".
Pupils did "not make enough progress in some year groups, particularly in reading and writing", Ofsted reported.
There were "not enough opportunities for pupils to write at length in all subjects". Less able learners did not always have enough time to finish their written work while in some lessons, the more able were "not sufficiently challenged". Pupils were also chattering and becoming easily distracted during lessons.
The school is smaller than average with 109 boys from the age of four to 11. Morning classes are devoted to Jewish studies. The afternoon is spent on the national curriculum. An above average number of boys have English as an "additional language".
Pupils enjoyed coming to school and made good progress in reception, Ofsted noted.
It recognised that Jewish studies made an "important contribution in teaching pupils about respect, rights and responsibilities".
"Requires improvement" is a grade below "good" but above "inadequate". It replaced the old category of "satisfactory" in 2012.