New York Governor David A. Paterson plans to eliminate nearly 9,000 jobs, mostly through layoffs, after failing to get unions to agree to cost-cutting concessions.

Paterson’s office hopes the threat will force unions to soften their stance. Otherwise, the cuts begin in July.

The cuts would affect 6.4% of the work force, not counting employees of public universities, who would not be included.

The Public Employees Federation responded to the call for layoffs by asking the state to hire more workers as a way to reduce overtime costs. Unions have also called for tax raises on the wealthy to prevent layoffs.

Paterson wants employees to forgo previously negotiated raises for the coming year, and to defer one week’s pay.