Conditional referential integrity with PostgreSQL

Consider a basic relational pattern (one parent, multiple children)

As part of a transaction, I may delete parents, but I may also re-insert them. In the first case, I want the foreign key to become NULL. In the second case, I would like to preserve the relational integrity. Is there a way to declare the foreign key so that it satisfies both requirements?

create table parent
(
  parent_id integer primary key
);

create table child
(
  child_id integer primary key,
  parent_id integer references parent (parent_id)
    on delete set null
);

insert into parent (parent_id) VALUES (1), (2), (3);
insert into child (child_id, parent_id) VALUES (1, 1), (2, 2), (3, 3);

BEGIN;
delete from parent where parent_id = 1;
COMMIT;
-- expecting NULL
select parent_id from child where child_id = 1;

BEGIN;
delete from parent where parent_id = 2;
insert into parent (parent_id) VALUES (2);
COMMIT;
-- would like 2, but getting NULL
select parent_id from child where child_id = 2;