Apex Class:

public class AccountExtensionController {

    public String redirectUrl {get; set;}
    public Boolean isRedirect {get; set;}
    private Account acc {get; set;}
    
    public AccountExtensionController(ApexPages.StandardController sc) {
        this.acc = (Account)sc.getRecord();
    }
    
    public PageReference redirectToNewContact() {
        isRedirect = true;
        redirectUrl = '/003/e?retURL=' + acc.Id + '&accid=' + acc.Id;
        return null;
    }
}

Visualforce Page:

<apex:page standardController="Account" extensions="AccountExtensionController" showHeader="false" sidebar="false">
    <apex:form >
        <apex:commandButton value="New Contact" action="{!redirectToNewContact}" rerender="redirectPanel" />
        <apex:outputPanel id="redirectPanel" >
            <apex:outputPanel rendered="{!isRedirect}">
                <!--redirect using javascript-->
                <script type="text/javascript">
                window.top.location.href = '{!redirectUrl}';
                </script>
            </apex:outputPanel>
        </apex:outputPanel>
    </apex:form>
</apex:page>