In a major report drawing together findings on Scottish schools over a four-year period, he highlighted "variable" standards in primary education.
Dr Maxwell said financial constraints had been a challenge for education.
But he said that, overall, inspectors had been impressed with the commitment shown by leaders and staff.
Dr Maxwell said he had found "many strengths" across all sectors of education and examples of "outstanding innovative practice".
The report - Quality and Improvement in Scottish Education 2012-2016 - set out five key areas for improvement:
Education inspectors said Scottish education had gone through a period of "very significant reform".
Speaking at Larbert High School, where the report was launched, Dr Maxwell said: "Overall, our inspectors have been impressed by the strong commitment of leaders and staff to improving outcomes for children and young people.
"High-quality leadership will be essential to ensuring that sufficient progress is made, across all sectors, in order to continue to secure improvements in education practice and achieve our national ambition of ensuring all learners can reach their potential, regardless of their background.
"We believe that addressing these five priority areas for improvement effectively will make a decisive contribution to achieving the twin aims of excellence and equity for Scottish learners which is at the heart of the National Improvement Framework."
EIS General Secretary Larry Flanagan said the report was a "substantial piece of work" which highlighted Â£the continuing strengths of Scotland's education system including the very high levels of commitment that are demonstrated by Scotland's teachers".
He added: "Education Scotland itself has to be more proactive in supporting schools and teachers.
"Criticism has been voiced by many members, for example, about poor support and a lack of communication around the introduction of new national qualifications.
"As a well-funded agency it needs to deliver that crucial support as well as provide a critical voice to government policy making, which should be evidenced based at all times."
"One thing that is very clear throughout the report is the degree of change compared to the scale of cuts throughout education, and this will continue to create challenges until the politics of austerity cease and education budgets are substantially increased."

Irish fell to a 15th defeat of the league season against Sale on Saturday to leave them four points adrift at the bottom with three games left.
Back row Narraway dismissed concerns at the spirit of his squad heading into the Premiership run-in.
"It's the one thing I think we have in abundance, accuracy and being clinical are things we haven't," he said.
"That's why we find ourselves here (at the bottom)," Narraway added. "Not because of the spirit or the want or desire not being there.
"It's just that 5-10% in terms of accuracy that probably a little bit of confidence gives us," the 32-year-old former Gloucester, Perpignan and England player said.
Irish face Harlequins in the quarter-finals of the European Challenge Cup at The Stoop on Saturday before their Premiership status will be determined in remaining games against Newcastle, Quins and Wasps.
The fixture against fellow strugglers Newcastle at Kingston Park on 17 April has been described as "a Grand Final" by Narraway, who said: "Newcastle is huge, they're one place above us, one win above us."
Scotland's Chief Education Inspector Bill Maxwell has said key aspects of education need to be improved.
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London Irish captain Luke Narraway says improving their accuracy is the missing piece to their Premiership survival.