The impulsive Volterra integral equation \[ (1)\quad x(t)=g(t)+\int^{t}_{0}H(t,s,x(s))ds+\sum_{0<t_ k<t}I_ k(x(t_ k)), \] and the impulsive differential equation \[ (2)\quad u'=f(t,u),\quad t\neq t_ i,\quad \Delta u|_{t=t_ i}=I_ i(u),\quad i=1,2,...,p,\quad u(0)=u_ 0, \] are studied in abstract cones. By suitably modifying the notions of upper and lower quasi- solutions, the existence of coupled minimal and maximal quasi-solutions of (1), (2) is proved. These turn out to be limits of monotonic sequences in a sector with respect to a normal cone.